Achawki3:

Claimed by Patrick Todd (Spring 2017) Claimed by Anthony Chawki (Fall 2017)

'''
==Definition==
'''Conductivity''' is the degree to which a specified material conducts electricity, calculated as the ratio of the current density in the material to the electric field that causes the flow of current. (It is the ''reciprocal'' of the resistivity.)

In other words, Conductivity is the measure of the ease at which an electric charge or heat can pass through a material.
'''Electrical conductivity''' tells us how well a material will allow electricity to travel through it.
'''Thermal conductivity''' tells us the ease upon which thermal energy (heat for most purposes) can move through a material.

==Symbols==

Electrical Conductivity is measured in siemens per meter and is often represented using the Greek letters '''σ''' (lowercase sigma), '''κ''' (kappa), or '''γ''' (lowercase gamma).

== SI Units ==

Conductivity's SI units is the siemens per metre, <math> A^{2} s^{3} m^{−3} kg^{−1} </math>(named after Werner von Siemens) or, more simply, <math>S m^{−1}</math>.

== Classification of Materials by Conductivity ==

Conductors, Semiconductors, and Insulators are the main three classifications of a material when talking about its electrical conductivity. Conductors are materials with high conductivity. Semiconductors have an in between level of conductivity, while insulators have low conductivity. Meaning if you want to pass a lot of electricity to something use a conductor, if you want to pass some electricity but also lower the original amount use a semiconductor, and if you want to cut the flow of electricity use an insulator. Provided below is a list of materials that fit into each category.

Conductors: Gold, Iron, Silver, Copper, Aluminum, Tin
Semiconductors: Silicon, Germanium
Insulators: Glass, Porcelain, Rubber, Cloth, Paper, Air

[[File:NatCopper.png|200px|thumb|left|Copper Conductor]]
[[File:Semiconductor-1.jpg|200px|thumb|left|Semiconductors]]
[[File:Rubber_band.jpg|200px|thumb|left|Rubber Insulator]]
[[File:plasma-ball-2282449_960_720.jpg|200px|thumb|left|Plasma]]

==Conductivity By Material Type==

===Metals===

Conductivity in metals decreases when temperature is increased. When the temperature increases, the resistance of the metal also increases linearly. As the temperature of a metal is reduced, the temperature dependence of resistivity follows a power law function of temperature.

The structure of metal is made up of a lattice of atoms. The outer shell of electrons that surround the parent atoms can come free and travel throughout the lattice, also known as an positive ionic lattice. A simpler definition of this phenomenon is the "sea" of electrons. This "sea" of electrons can move throughout the metal structure and conduct an electrical current. The electric field created by the electric potential cause the electrons to move to the positive terminal. The electrons are packed so densely that the electromagnetic field can travel at the speed of light with each electron having a small drift velocity.

The resistance in metals are created by temperature, the cross sectional area, the length, and the speed of vibration of the crystal lattice. The more resistance that is present the less conductive the metal is. The temperature causes irregularities in the lattice. If the cross sectional area is bigger then there is more electrons per unit length are available to carry current. Therefore, the smaller the cross sectional area the more resistance in the wire. The longer the wire the more likely scattering events take place. The more scattering events the higher the resistance in the wire. Impurities in the metal increase resistance too. The different ions in the metal create irregularities, which in turn create a vibration in the metal.

=== Semiconductors ===

Semiconductors are materials that have a conductivity in-between that of an insulator and a conductor. Their electrical resistance are much higher than ordinary conductors but still much lower than most insulators. Interestingly enough, their resistance decreases as their temperature increases, which is behavior opposite to that of a metal (insulator).

==== Temperature Dependence ====

Conductivity of a material is determined by two factors: the concentration of free carriers available
to conduct current and their mobility (or freedom to move). In a semiconductor, both mobility and
carrier concentration are temperature dependent.
As temperature increases, the electrical resistivity of metals increases. This is a reason why when computers heat up, they tend to slow down. Some materials exhibit superconductivity at extremely low temperatures. Below a certain temperature, resistivity vanishes, such as Pb (Lead) at 7.20 K.

===Plasma===

Plasma is a very good electrical conductor. Its electric potential is a special potential called plasma or space potential. It exists in the space between charged particles. If an electrode was put inside the plasma the potential would drop a considerable amount compared to the plasma potential because of a phenomenon called Debye sheath. The high conductivity results in relatively small electric fields.

==Superconductors==
[[File:Meissner_effect_p1390048.jpg|300px|thumb|right|Meissner Effect on Superconductor]]
Lowering the temperature of a metallic conductor will decrease the electrical resistance. The metal can be cooled gradually until the resistance is almost zero. Once the temperature drops past the critical temperature the resistance drops to zero. The zero resistance can allow the metal to have electrical current flow in a loop indefinitely without a power source.

===Applications of a Superconductor===

*Magnetic Resonance Imaging (MRI) and Nuclear Magnetic Resonance (NMR)
*Particle Accelerators and Magnetic Fusion Devices
*Electric Motors and Generators
*Supermagnets
*Digital Devices

==Band Theory==

==Equations==

'''Conductivity Relationship to Resistivity'''

<math>σ=1/ρ</math>

σ= Conductivity
ρ= Electric Resistivity

'''Maxwell's Equation for Electric Conductivity'''

<math>J=σE</math>

J= Electric Current Density
E= Electric Field
σ= Conductivity

Electric current density can be thought of as the electric current per cross sectional area of a specific material. Therefore this formula relates to each material differently. Every material has a specific conductivity associated with it, and this conductivity can help describe the electric field in each material. For example, materials such as copper and silver have extremely high electric conductivity and therefore in order to not have an almost infinite electric current density we can approximate the electric field inside the metals to be zero. This equation is essentially the proof for all metals having a zero electric field on the inside. The relationship between these three variables is known as Ohm's Law.

'''Poulliet's Law of Resistivity'''[[File:Resistivity_geometry.png|220px|thumb|right|Section of resistive material with a cross section and length.]]

<math>R=ρℓ/A </math>

R = Electric Resistance
ρ = Electric Resistivity
ℓ = Length
A = Cross-Sectional Area

Poulliet's Law states that a given material's resistance will increase in length, while it will decrease with an increase in Area. The SI unit for this law is Ohm*meter. The electrical resistivity is different for every substance.

==Conductivity in Real Life==

Conductors are used to carry electricity, as well as electrical signals in circuits.
Complementary metal–oxide–semiconductors, or CMOS for short, are the foundational building block of gate based logic circuits, that make up the majority of all modern electronics. CMOS circuits are composed of a combination of p-type and n-type semiconductors. These semiconductors will change their conductivity, based on the applied voltage, allowing for logic of 0's and 1's, or low voltage and high voltage, to be transferred through logical circuits. This allows us to apply boolean logic to circuits, such as AND and OR logic, or even create an amalgamation of AND's and OR's to create electronics, such as multiplexors, switches, latches, registers, decoders, encoders, etc.

=== Fun Examples ===
[https://www.youtube.com/watch?v=ODbgKXFED5o Salt Water Conductivity Experiment]

[https://www.youtube.com/watch?v=HaQnlftxQUU Fruit Conductivity Experiment]

[https://www.youtube.com/watch?v=zPqEEZa2Gis| Superconductor Experiment]

===Mathematical Problems===
====Simple====
Find the Conductivity of a material with an electrical field of <math>5*10^{12} (E = 5*10^{12})</math> and a current density of <math>5*10^2
(J = 5*10^2)</math>.
{| class="wikitable mw-collapsible mw-collapsed"
! Answer
|-
| <math> =10^{10} </math>
|}

====Medium====
Find the Resistivity of a wire with the resistance of <math>0.69Ω*m (R=0.69Ω*m)</math>, length of <math>10m (ℓ=10m)</math>, and cross-sectional area of <math>100m^{2} (A=100m^{2})</math>.
{| class="wikitable mw-collapsible mw-collapsed"
! Answer
|-
| 690 = 10ρ
|-
| ρ = 69
|}

==History==
'''Stephen Gray, Father of Conduction'''

''Born 1666 in Canterbury, England.''
''Died 1736 in London, England.''

Gray was an innovative thinker who performed many a experiment including work with the transmission of electricity. One day while performing one of his experiments, unbeknownst to him he discovered the difference between insulators and conductors. He was working with transmitting electricity and he changed the transmission wire from silk to brass wire when he noticed that electricity passes completely different in brass than it does in silk. After said discovery, Gray spend the next 3 years with the help of friends and family doing more research in similar topics, and with this research some might say solidified his name as the father of conduction.

'''Claude Pouillet, Pouillet's Law'''

''Born February 16, 1720 in Cusance, France.''
''Died June 14, 1868 in Paris, France.''

Claude was one of the earliest scientists to examine the Sun's influence on Earth's atmosphere, beyond simple radiation. After approximating the solar constant to be 1228 <math> W/m^{2} </math>, which turned out to be extremely close to the now recognized constant of 1367 <math> W/m^{2} </math>. This success earned him a chair in the Physics department at the École Normale Supérieure. From there he went on to design and create early, operational versions of sine and tangent galvanometers which measure current (more commonly known as an ammeter).

===Further reading===

[http://www.mse.gatech.edu/research/equipment-facilities/electrical-properties-materials-and-devices Georgia Tech Research and Information regarding conduction in School of Materials Science and Engineering]

[http://hyperphysics.phy-astr.gsu.edu/hbase/electric/resis.html HyperPhysics Explanations]

[https://en.wikipedia.org/wiki/Portal:Physics| Physics Portal]

===External links===
[http://www.physics4kids.com/files/elec_conduct.html Beginner Explanation]

[http://formulas.tutorvista.com/physics/thermal-conductivity-formula.html Thermal Conductivity]

[http://britneyspears.ac/physics/basics/basics.htm Brittany Spears explains semiconductors]

Conductivity

2017-11-29T21:48:37Z

Achawki3: /* Further reading */

Claimed by Patrick Todd (Spring 2017) Claimed by Anthony Chawki (Fall 2017)

'''
==Definition==
'''Conductivity''' is the degree to which a specified material conducts electricity, calculated as the ratio of the current density in the material to the electric field that causes the flow of current. (It is the ''reciprocal'' of the resistivity.)

In other words, Conductivity is the measure of the ease at which an electric charge or heat can pass through a material.
'''Electrical conductivity''' tells us how well a material will allow electricity to travel through it.
'''Thermal conductivity''' tells us the ease upon which thermal energy (heat for most purposes) can move through a material.

==Symbols==

Electrical Conductivity is measured in siemens per meter and is often represented using the Greek letters '''σ''' (lowercase sigma), '''κ''' (kappa), or '''γ''' (lowercase gamma).

== SI Units ==

Conductivity's SI units is the siemens per metre, <math> A^{2} s^{3} m^{−3} kg^{−1} </math>(named after Werner von Siemens) or, more simply, <math>S m^{−1}</math>.

== Classification of Materials by Conductivity ==

Conductors, Semiconductors, and Insulators are the main three classifications of a material when talking about its electrical conductivity. Conductors are materials with high conductivity. Semiconductors have an in between level of conductivity, while insulators have low conductivity. Meaning if you want to pass a lot of electricity to something use a conductor, if you want to pass some electricity but also lower the original amount use a semiconductor, and if you want to cut the flow of electricity use an insulator. Provided below is a list of materials that fit into each category.

Conductors: Gold, Iron, Silver, Copper, Aluminum, Tin
Semiconductors: Silicon, Germanium
Insulators: Glass, Porcelain, Rubber, Cloth, Paper, Air

[[File:NatCopper.png|200px|thumb|left|Copper Conductor]]
[[File:Semiconductor-1.jpg|200px|thumb|left|Semiconductors]]
[[File:Rubber_band.jpg|200px|thumb|left|Rubber Insulator]]
[[File:plasma-ball-2282449_960_720.jpg|200px|thumb|left|Plasma]]

==Conductivity By Material Type==

===Metals===

Conductivity in metals decreases when temperature is increased. When the temperature increases, the resistance of the metal also increases linearly. As the temperature of a metal is reduced, the temperature dependence of resistivity follows a power law function of temperature.

The structure of metal is made up of a lattice of atoms. The outer shell of electrons that surround the parent atoms can come free and travel throughout the lattice, also known as an positive ionic lattice. A simpler definition of this phenomenon is the "sea" of electrons. This "sea" of electrons can move throughout the metal structure and conduct an electrical current. The electric field created by the electric potential cause the electrons to move to the positive terminal. The electrons are packed so densely that the electromagnetic field can travel at the speed of light with each electron having a small drift velocity.

The resistance in metals are created by temperature, the cross sectional area, the length, and the speed of vibration of the crystal lattice. The more resistance that is present the less conductive the metal is. The temperature causes irregularities in the lattice. If the cross sectional area is bigger then there is more electrons per unit length are available to carry current. Therefore, the smaller the cross sectional area the more resistance in the wire. The longer the wire the more likely scattering events take place. The more scattering events the higher the resistance in the wire. Impurities in the metal increase resistance too. The different ions in the metal create irregularities, which in turn create a vibration in the metal.

=== Semiconductors ===

Semiconductors are materials that have a conductivity in-between that of an insulator and a conductor. Their electrical resistance are much higher than ordinary conductors but still much lower than most insulators. Interestingly enough, their resistance decreases as their temperature increases, which is behavior opposite to that of a metal (insulator).

==== Temperature Dependence ====

Conductivity of a material is determined by two factors: the concentration of free carriers available
to conduct current and their mobility (or freedom to move). In a semiconductor, both mobility and
carrier concentration are temperature dependent.
As temperature increases, the electrical resistivity of metals increases. This is a reason why when computers heat up, they tend to slow down. Some materials exhibit superconductivity at extremely low temperatures. Below a certain temperature, resistivity vanishes, such as Pb (Lead) at 7.20 K.

===Plasma===

Plasma is a very good electrical conductor. Its electric potential is a special potential called plasma or space potential. It exists in the space between charged particles. If an electrode was put inside the plasma the potential would drop a considerable amount compared to the plasma potential because of a phenomenon called Debye sheath. The high conductivity results in relatively small electric fields.

==Superconductors==
[[File:Meissner_effect_p1390048.jpg|300px|thumb|right|Meissner Effect on Superconductor]]
Lowering the temperature of a metallic conductor will decrease the electrical resistance. The metal can be cooled gradually until the resistance is almost zero. Once the temperature drops past the critical temperature the resistance drops to zero. The zero resistance can allow the metal to have electrical current flow in a loop indefinitely without a power source.

===Applications of a Superconductor===

*Magnetic Resonance Imaging (MRI) and Nuclear Magnetic Resonance (NMR)
*Particle Accelerators and Magnetic Fusion Devices
*Electric Motors and Generators
*Supermagnets
*Digital Devices

==Band Theory==

==Equations==

'''Conductivity Relationship to Resistivity'''

<math>σ=1/ρ</math>

σ= Conductivity
ρ= Electric Resistivity

'''Maxwell's Equation for Electric Conductivity'''

<math>J=σE</math>

J= Electric Current Density
E= Electric Field
σ= Conductivity

Electric current density can be thought of as the electric current per cross sectional area of a specific material. Therefore this formula relates to each material differently. Every material has a specific conductivity associated with it, and this conductivity can help describe the electric field in each material. For example, materials such as copper and silver have extremely high electric conductivity and therefore in order to not have an almost infinite electric current density we can approximate the electric field inside the metals to be zero. This equation is essentially the proof for all metals having a zero electric field on the inside. The relationship between these three variables is known as Ohm's Law.

'''Poulliet's Law of Resistivity'''[[File:Resistivity_geometry.png|220px|thumb|right|Section of resistive material with a cross section and length.]]

<math>R=ρℓ/A </math>

R = Electric Resistance
ρ = Electric Resistivity
ℓ = Length
A = Cross-Sectional Area

Poulliet's Law states that a given material's resistance will increase in length, while it will decrease with an increase in Area. The SI unit for this law is Ohm*meter. The electrical resistivity is different for every substance.

==Conductivity in Real Life==

Conductors are used to carry electricity, as well as electrical signals in circuits.
Complementary metal–oxide–semiconductors, or CMOS for short, are the foundational building block of gate based logic circuits, that make up the majority of all modern electronics. CMOS circuits are composed of a combination of p-type and n-type semiconductors. These semiconductors will change their conductivity, based on the applied voltage, allowing for logic of 0's and 1's, or low voltage and high voltage, to be transferred through logical circuits. This allows us to apply boolean logic to circuits, such as AND and OR logic, or even create an amalgamation of AND's and OR's to create electronics, such as multiplexors, switches, latches, registers, decoders, encoders, etc.

=== Fun Examples ===
[https://www.youtube.com/watch?v=ODbgKXFED5o Salt Water Conductivity Experiment]

[https://www.youtube.com/watch?v=HaQnlftxQUU Fruit Conductivity Experiment]

===Mathematical Problems===
====Simple====
Find the Conductivity of a material with an electrical field of <math>5*10^{12} (E = 5*10^{12})</math> and a current density of <math>5*10^2
(J = 5*10^2)</math>.
{| class="wikitable mw-collapsible mw-collapsed"
! Answer
|-
| <math> =10^{10} </math>
|}

====Medium====
Find the Resistivity of a wire with the resistance of <math>0.69Ω*m (R=0.69Ω*m)</math>, length of <math>10m (ℓ=10m)</math>, and cross-sectional area of <math>100m^{2} (A=100m^{2})</math>.
{| class="wikitable mw-collapsible mw-collapsed"
! Answer
|-
| 690 = 10ρ
|-
| ρ = 69
|}

==History==
'''Stephen Gray, Father of Conduction'''

''Born 1666 in Canterbury, England.''
''Died 1736 in London, England.''

Gray was an innovative thinker who performed many a experiment including work with the transmission of electricity. One day while performing one of his experiments, unbeknownst to him he discovered the difference between insulators and conductors. He was working with transmitting electricity and he changed the transmission wire from silk to brass wire when he noticed that electricity passes completely different in brass than it does in silk. After said discovery, Gray spend the next 3 years with the help of friends and family doing more research in similar topics, and with this research some might say solidified his name as the father of conduction.

'''Claude Pouillet, Pouillet's Law'''

''Born February 16, 1720 in Cusance, France.''
''Died June 14, 1868 in Paris, France.''

Claude was one of the earliest scientists to examine the Sun's influence on Earth's atmosphere, beyond simple radiation. After approximating the solar constant to be 1228 <math> W/m^{2} </math>, which turned out to be extremely close to the now recognized constant of 1367 <math> W/m^{2} </math>. This success earned him a chair in the Physics department at the École Normale Supérieure. From there he went on to design and create early, operational versions of sine and tangent galvanometers which measure current (more commonly known as an ammeter).

===Further reading===

[http://www.mse.gatech.edu/research/equipment-facilities/electrical-properties-materials-and-devices Georgia Tech Research and Information regarding conduction in School of Materials Science and Engineering]

[http://hyperphysics.phy-astr.gsu.edu/hbase/electric/resis.html HyperPhysics Explanations]

[https://en.wikipedia.org/wiki/Portal:Physics| Physics Portal]

===External links===
[http://www.physics4kids.com/files/elec_conduct.html Beginner Explanation]

[http://formulas.tutorvista.com/physics/thermal-conductivity-formula.html Thermal Conductivity]

[http://britneyspears.ac/physics/basics/basics.htm Brittany Spears explains semiconductors]

Conductivity

2017-11-29T21:48:21Z

Achawki3: /* Further reading */

Claimed by Patrick Todd (Spring 2017) Claimed by Anthony Chawki (Fall 2017)

'''
==Definition==
'''Conductivity''' is the degree to which a specified material conducts electricity, calculated as the ratio of the current density in the material to the electric field that causes the flow of current. (It is the ''reciprocal'' of the resistivity.)

In other words, Conductivity is the measure of the ease at which an electric charge or heat can pass through a material.
'''Electrical conductivity''' tells us how well a material will allow electricity to travel through it.
'''Thermal conductivity''' tells us the ease upon which thermal energy (heat for most purposes) can move through a material.

==Symbols==

Electrical Conductivity is measured in siemens per meter and is often represented using the Greek letters '''σ''' (lowercase sigma), '''κ''' (kappa), or '''γ''' (lowercase gamma).

== SI Units ==

Conductivity's SI units is the siemens per metre, <math> A^{2} s^{3} m^{−3} kg^{−1} </math>(named after Werner von Siemens) or, more simply, <math>S m^{−1}</math>.

== Classification of Materials by Conductivity ==

Conductors, Semiconductors, and Insulators are the main three classifications of a material when talking about its electrical conductivity. Conductors are materials with high conductivity. Semiconductors have an in between level of conductivity, while insulators have low conductivity. Meaning if you want to pass a lot of electricity to something use a conductor, if you want to pass some electricity but also lower the original amount use a semiconductor, and if you want to cut the flow of electricity use an insulator. Provided below is a list of materials that fit into each category.

Conductors: Gold, Iron, Silver, Copper, Aluminum, Tin
Semiconductors: Silicon, Germanium
Insulators: Glass, Porcelain, Rubber, Cloth, Paper, Air

[[File:NatCopper.png|200px|thumb|left|Copper Conductor]]
[[File:Semiconductor-1.jpg|200px|thumb|left|Semiconductors]]
[[File:Rubber_band.jpg|200px|thumb|left|Rubber Insulator]]
[[File:plasma-ball-2282449_960_720.jpg|200px|thumb|left|Plasma]]

==Conductivity By Material Type==

===Metals===

Conductivity in metals decreases when temperature is increased. When the temperature increases, the resistance of the metal also increases linearly. As the temperature of a metal is reduced, the temperature dependence of resistivity follows a power law function of temperature.

The structure of metal is made up of a lattice of atoms. The outer shell of electrons that surround the parent atoms can come free and travel throughout the lattice, also known as an positive ionic lattice. A simpler definition of this phenomenon is the "sea" of electrons. This "sea" of electrons can move throughout the metal structure and conduct an electrical current. The electric field created by the electric potential cause the electrons to move to the positive terminal. The electrons are packed so densely that the electromagnetic field can travel at the speed of light with each electron having a small drift velocity.

The resistance in metals are created by temperature, the cross sectional area, the length, and the speed of vibration of the crystal lattice. The more resistance that is present the less conductive the metal is. The temperature causes irregularities in the lattice. If the cross sectional area is bigger then there is more electrons per unit length are available to carry current. Therefore, the smaller the cross sectional area the more resistance in the wire. The longer the wire the more likely scattering events take place. The more scattering events the higher the resistance in the wire. Impurities in the metal increase resistance too. The different ions in the metal create irregularities, which in turn create a vibration in the metal.

=== Semiconductors ===

Semiconductors are materials that have a conductivity in-between that of an insulator and a conductor. Their electrical resistance are much higher than ordinary conductors but still much lower than most insulators. Interestingly enough, their resistance decreases as their temperature increases, which is behavior opposite to that of a metal (insulator).

==== Temperature Dependence ====

Conductivity of a material is determined by two factors: the concentration of free carriers available
to conduct current and their mobility (or freedom to move). In a semiconductor, both mobility and
carrier concentration are temperature dependent.
As temperature increases, the electrical resistivity of metals increases. This is a reason why when computers heat up, they tend to slow down. Some materials exhibit superconductivity at extremely low temperatures. Below a certain temperature, resistivity vanishes, such as Pb (Lead) at 7.20 K.

===Plasma===

Plasma is a very good electrical conductor. Its electric potential is a special potential called plasma or space potential. It exists in the space between charged particles. If an electrode was put inside the plasma the potential would drop a considerable amount compared to the plasma potential because of a phenomenon called Debye sheath. The high conductivity results in relatively small electric fields.

==Superconductors==
[[File:Meissner_effect_p1390048.jpg|300px|thumb|right|Meissner Effect on Superconductor]]
Lowering the temperature of a metallic conductor will decrease the electrical resistance. The metal can be cooled gradually until the resistance is almost zero. Once the temperature drops past the critical temperature the resistance drops to zero. The zero resistance can allow the metal to have electrical current flow in a loop indefinitely without a power source.

===Applications of a Superconductor===

*Magnetic Resonance Imaging (MRI) and Nuclear Magnetic Resonance (NMR)
*Particle Accelerators and Magnetic Fusion Devices
*Electric Motors and Generators
*Supermagnets
*Digital Devices

==Band Theory==

==Equations==

'''Conductivity Relationship to Resistivity'''

<math>σ=1/ρ</math>

σ= Conductivity
ρ= Electric Resistivity

'''Maxwell's Equation for Electric Conductivity'''

<math>J=σE</math>

J= Electric Current Density
E= Electric Field
σ= Conductivity

Electric current density can be thought of as the electric current per cross sectional area of a specific material. Therefore this formula relates to each material differently. Every material has a specific conductivity associated with it, and this conductivity can help describe the electric field in each material. For example, materials such as copper and silver have extremely high electric conductivity and therefore in order to not have an almost infinite electric current density we can approximate the electric field inside the metals to be zero. This equation is essentially the proof for all metals having a zero electric field on the inside. The relationship between these three variables is known as Ohm's Law.

'''Poulliet's Law of Resistivity'''[[File:Resistivity_geometry.png|220px|thumb|right|Section of resistive material with a cross section and length.]]

<math>R=ρℓ/A </math>

R = Electric Resistance
ρ = Electric Resistivity
ℓ = Length
A = Cross-Sectional Area

Poulliet's Law states that a given material's resistance will increase in length, while it will decrease with an increase in Area. The SI unit for this law is Ohm*meter. The electrical resistivity is different for every substance.

==Conductivity in Real Life==

Conductors are used to carry electricity, as well as electrical signals in circuits.
Complementary metal–oxide–semiconductors, or CMOS for short, are the foundational building block of gate based logic circuits, that make up the majority of all modern electronics. CMOS circuits are composed of a combination of p-type and n-type semiconductors. These semiconductors will change their conductivity, based on the applied voltage, allowing for logic of 0's and 1's, or low voltage and high voltage, to be transferred through logical circuits. This allows us to apply boolean logic to circuits, such as AND and OR logic, or even create an amalgamation of AND's and OR's to create electronics, such as multiplexors, switches, latches, registers, decoders, encoders, etc.

=== Fun Examples ===
[https://www.youtube.com/watch?v=ODbgKXFED5o Salt Water Conductivity Experiment]

[https://www.youtube.com/watch?v=HaQnlftxQUU Fruit Conductivity Experiment]

===Mathematical Problems===
====Simple====
Find the Conductivity of a material with an electrical field of <math>5*10^{12} (E = 5*10^{12})</math> and a current density of <math>5*10^2
(J = 5*10^2)</math>.
{| class="wikitable mw-collapsible mw-collapsed"
! Answer
|-
| <math> =10^{10} </math>
|}

====Medium====
Find the Resistivity of a wire with the resistance of <math>0.69Ω*m (R=0.69Ω*m)</math>, length of <math>10m (ℓ=10m)</math>, and cross-sectional area of <math>100m^{2} (A=100m^{2})</math>.
{| class="wikitable mw-collapsible mw-collapsed"
! Answer
|-
| 690 = 10ρ
|-
| ρ = 69
|}

==History==
'''Stephen Gray, Father of Conduction'''

''Born 1666 in Canterbury, England.''
''Died 1736 in London, England.''

Gray was an innovative thinker who performed many a experiment including work with the transmission of electricity. One day while performing one of his experiments, unbeknownst to him he discovered the difference between insulators and conductors. He was working with transmitting electricity and he changed the transmission wire from silk to brass wire when he noticed that electricity passes completely different in brass than it does in silk. After said discovery, Gray spend the next 3 years with the help of friends and family doing more research in similar topics, and with this research some might say solidified his name as the father of conduction.

'''Claude Pouillet, Pouillet's Law'''

''Born February 16, 1720 in Cusance, France.''
''Died June 14, 1868 in Paris, France.''

Claude was one of the earliest scientists to examine the Sun's influence on Earth's atmosphere, beyond simple radiation. After approximating the solar constant to be 1228 <math> W/m^{2} </math>, which turned out to be extremely close to the now recognized constant of 1367 <math> W/m^{2} </math>. This success earned him a chair in the Physics department at the École Normale Supérieure. From there he went on to design and create early, operational versions of sine and tangent galvanometers which measure current (more commonly known as an ammeter).

===Further reading===

[http://www.mse.gatech.edu/research/equipment-facilities/electrical-properties-materials-and-devices Georgia Tech Research and Information regarding conduction in School of Materials Science and Engineering]

[http://hyperphysics.phy-astr.gsu.edu/hbase/electric/resis.html HyperPhysics Explanations]

[https://en.wikipedia.org/wiki/Portal:Physics|Physics Portal]

===External links===
[http://www.physics4kids.com/files/elec_conduct.html Beginner Explanation]

[http://formulas.tutorvista.com/physics/thermal-conductivity-formula.html Thermal Conductivity]

[http://britneyspears.ac/physics/basics/basics.htm Brittany Spears explains semiconductors]

Conductivity

2017-11-29T21:46:55Z

Achawki3:

Claimed by Patrick Todd (Spring 2017) Claimed by Anthony Chawki (Fall 2017)

'''
==Definition==
'''Conductivity''' is the degree to which a specified material conducts electricity, calculated as the ratio of the current density in the material to the electric field that causes the flow of current. (It is the ''reciprocal'' of the resistivity.)

In other words, Conductivity is the measure of the ease at which an electric charge or heat can pass through a material.
'''Electrical conductivity''' tells us how well a material will allow electricity to travel through it.
'''Thermal conductivity''' tells us the ease upon which thermal energy (heat for most purposes) can move through a material.

==Symbols==

Electrical Conductivity is measured in siemens per meter and is often represented using the Greek letters '''σ''' (lowercase sigma), '''κ''' (kappa), or '''γ''' (lowercase gamma).

== SI Units ==

Conductivity's SI units is the siemens per metre, <math> A^{2} s^{3} m^{−3} kg^{−1} </math>(named after Werner von Siemens) or, more simply, <math>S m^{−1}</math>.

== Classification of Materials by Conductivity ==

Conductors, Semiconductors, and Insulators are the main three classifications of a material when talking about its electrical conductivity. Conductors are materials with high conductivity. Semiconductors have an in between level of conductivity, while insulators have low conductivity. Meaning if you want to pass a lot of electricity to something use a conductor, if you want to pass some electricity but also lower the original amount use a semiconductor, and if you want to cut the flow of electricity use an insulator. Provided below is a list of materials that fit into each category.

Conductors: Gold, Iron, Silver, Copper, Aluminum, Tin
Semiconductors: Silicon, Germanium
Insulators: Glass, Porcelain, Rubber, Cloth, Paper, Air

[[File:NatCopper.png|200px|thumb|left|Copper Conductor]]
[[File:Semiconductor-1.jpg|200px|thumb|left|Semiconductors]]
[[File:Rubber_band.jpg|200px|thumb|left|Rubber Insulator]]
[[File:plasma-ball-2282449_960_720.jpg|200px|thumb|left|Plasma]]

==Conductivity By Material Type==

===Metals===

Conductivity in metals decreases when temperature is increased. When the temperature increases, the resistance of the metal also increases linearly. As the temperature of a metal is reduced, the temperature dependence of resistivity follows a power law function of temperature.

The structure of metal is made up of a lattice of atoms. The outer shell of electrons that surround the parent atoms can come free and travel throughout the lattice, also known as an positive ionic lattice. A simpler definition of this phenomenon is the "sea" of electrons. This "sea" of electrons can move throughout the metal structure and conduct an electrical current. The electric field created by the electric potential cause the electrons to move to the positive terminal. The electrons are packed so densely that the electromagnetic field can travel at the speed of light with each electron having a small drift velocity.

The resistance in metals are created by temperature, the cross sectional area, the length, and the speed of vibration of the crystal lattice. The more resistance that is present the less conductive the metal is. The temperature causes irregularities in the lattice. If the cross sectional area is bigger then there is more electrons per unit length are available to carry current. Therefore, the smaller the cross sectional area the more resistance in the wire. The longer the wire the more likely scattering events take place. The more scattering events the higher the resistance in the wire. Impurities in the metal increase resistance too. The different ions in the metal create irregularities, which in turn create a vibration in the metal.

=== Semiconductors ===

Semiconductors are materials that have a conductivity in-between that of an insulator and a conductor. Their electrical resistance are much higher than ordinary conductors but still much lower than most insulators. Interestingly enough, their resistance decreases as their temperature increases, which is behavior opposite to that of a metal (insulator).

==== Temperature Dependence ====

Conductivity of a material is determined by two factors: the concentration of free carriers available
to conduct current and their mobility (or freedom to move). In a semiconductor, both mobility and
carrier concentration are temperature dependent.
As temperature increases, the electrical resistivity of metals increases. This is a reason why when computers heat up, they tend to slow down. Some materials exhibit superconductivity at extremely low temperatures. Below a certain temperature, resistivity vanishes, such as Pb (Lead) at 7.20 K.

===Plasma===

Plasma is a very good electrical conductor. Its electric potential is a special potential called plasma or space potential. It exists in the space between charged particles. If an electrode was put inside the plasma the potential would drop a considerable amount compared to the plasma potential because of a phenomenon called Debye sheath. The high conductivity results in relatively small electric fields.

==Superconductors==
[[File:Meissner_effect_p1390048.jpg|300px|thumb|right|Meissner Effect on Superconductor]]
Lowering the temperature of a metallic conductor will decrease the electrical resistance. The metal can be cooled gradually until the resistance is almost zero. Once the temperature drops past the critical temperature the resistance drops to zero. The zero resistance can allow the metal to have electrical current flow in a loop indefinitely without a power source.

===Applications of a Superconductor===

*Magnetic Resonance Imaging (MRI) and Nuclear Magnetic Resonance (NMR)
*Particle Accelerators and Magnetic Fusion Devices
*Electric Motors and Generators
*Supermagnets
*Digital Devices

==Band Theory==

==Equations==

'''Conductivity Relationship to Resistivity'''

<math>σ=1/ρ</math>

σ= Conductivity
ρ= Electric Resistivity

'''Maxwell's Equation for Electric Conductivity'''

<math>J=σE</math>

J= Electric Current Density
E= Electric Field
σ= Conductivity

Electric current density can be thought of as the electric current per cross sectional area of a specific material. Therefore this formula relates to each material differently. Every material has a specific conductivity associated with it, and this conductivity can help describe the electric field in each material. For example, materials such as copper and silver have extremely high electric conductivity and therefore in order to not have an almost infinite electric current density we can approximate the electric field inside the metals to be zero. This equation is essentially the proof for all metals having a zero electric field on the inside. The relationship between these three variables is known as Ohm's Law.

'''Poulliet's Law of Resistivity'''[[File:Resistivity_geometry.png|220px|thumb|right|Section of resistive material with a cross section and length.]]

<math>R=ρℓ/A </math>

R = Electric Resistance
ρ = Electric Resistivity
ℓ = Length
A = Cross-Sectional Area

Poulliet's Law states that a given material's resistance will increase in length, while it will decrease with an increase in Area. The SI unit for this law is Ohm*meter. The electrical resistivity is different for every substance.

==Conductivity in Real Life==

Conductors are used to carry electricity, as well as electrical signals in circuits.
Complementary metal–oxide–semiconductors, or CMOS for short, are the foundational building block of gate based logic circuits, that make up the majority of all modern electronics. CMOS circuits are composed of a combination of p-type and n-type semiconductors. These semiconductors will change their conductivity, based on the applied voltage, allowing for logic of 0's and 1's, or low voltage and high voltage, to be transferred through logical circuits. This allows us to apply boolean logic to circuits, such as AND and OR logic, or even create an amalgamation of AND's and OR's to create electronics, such as multiplexors, switches, latches, registers, decoders, encoders, etc.

=== Fun Examples ===
[https://www.youtube.com/watch?v=ODbgKXFED5o Salt Water Conductivity Experiment]

[https://www.youtube.com/watch?v=HaQnlftxQUU Fruit Conductivity Experiment]

===Mathematical Problems===
====Simple====
Find the Conductivity of a material with an electrical field of <math>5*10^{12} (E = 5*10^{12})</math> and a current density of <math>5*10^2
(J = 5*10^2)</math>.
{| class="wikitable mw-collapsible mw-collapsed"
! Answer
|-
| <math> =10^{10} </math>
|}

====Medium====
Find the Resistivity of a wire with the resistance of <math>0.69Ω*m (R=0.69Ω*m)</math>, length of <math>10m (ℓ=10m)</math>, and cross-sectional area of <math>100m^{2} (A=100m^{2})</math>.
{| class="wikitable mw-collapsible mw-collapsed"
! Answer
|-
| 690 = 10ρ
|-
| ρ = 69
|}

==History==
'''Stephen Gray, Father of Conduction'''

''Born 1666 in Canterbury, England.''
''Died 1736 in London, England.''

Gray was an innovative thinker who performed many a experiment including work with the transmission of electricity. One day while performing one of his experiments, unbeknownst to him he discovered the difference between insulators and conductors. He was working with transmitting electricity and he changed the transmission wire from silk to brass wire when he noticed that electricity passes completely different in brass than it does in silk. After said discovery, Gray spend the next 3 years with the help of friends and family doing more research in similar topics, and with this research some might say solidified his name as the father of conduction.

'''Claude Pouillet, Pouillet's Law'''

''Born February 16, 1720 in Cusance, France.''
''Died June 14, 1868 in Paris, France.''

Claude was one of the earliest scientists to examine the Sun's influence on Earth's atmosphere, beyond simple radiation. After approximating the solar constant to be 1228 <math> W/m^{2} </math>, which turned out to be extremely close to the now recognized constant of 1367 <math> W/m^{2} </math>. This success earned him a chair in the Physics department at the École Normale Supérieure. From there he went on to design and create early, operational versions of sine and tangent galvanometers which measure current (more commonly known as an ammeter).

===Further reading===

[http://www.mse.gatech.edu/research/equipment-facilities/electrical-properties-materials-and-devices Georgia Tech Research and Information regarding conduction in School of Materials Science and Engineering]

[http://hyperphysics.phy-astr.gsu.edu/hbase/electric/resis.html HyperPhysics Explanations]

===External links===
[http://www.physics4kids.com/files/elec_conduct.html Beginner Explanation]

[http://formulas.tutorvista.com/physics/thermal-conductivity-formula.html Thermal Conductivity]

[http://britneyspears.ac/physics/basics/basics.htm Brittany Spears explains semiconductors]

File:Meissner effect p1390048.jpg

2017-11-29T21:43:34Z

Achawki3:

Conductivity

2017-11-29T21:23:09Z

Achawki3:

Claimed by Patrick Todd (Spring 2017) Claimed by Anthony Chawki (Fall 2017)

'''
==Definition==
'''Conductivity''' is the degree to which a specified material conducts electricity, calculated as the ratio of the current density in the material to the electric field that causes the flow of current. (It is the ''reciprocal'' of the resistivity.)

In other words, Conductivity is the measure of the ease at which an electric charge or heat can pass through a material.
'''Electrical conductivity''' tells us how well a material will allow electricity to travel through it.
'''Thermal conductivity''' tells us the ease upon which thermal energy (heat for most purposes) can move through a material.

==Symbols==

Electrical Conductivity is measured in siemens per meter and is often represented using the Greek letters '''σ''' (lowercase sigma), '''κ''' (kappa), or '''γ''' (lowercase gamma).

== SI Units ==

Conductivity's SI units is the siemens per metre, <math> A^{2} s^{3} m^{−3} kg^{−1} </math>(named after Werner von Siemens) or, more simply, <math>S m^{−1}</math>.

== Classification of Materials by Conductivity ==

Conductors, Semiconductors, and Insulators are the main three classifications of a material when talking about its electrical conductivity. Conductors are materials with high conductivity. Semiconductors have an in between level of conductivity, while insulators have low conductivity. Meaning if you want to pass a lot of electricity to something use a conductor, if you want to pass some electricity but also lower the original amount use a semiconductor, and if you want to cut the flow of electricity use an insulator. Provided below is a list of materials that fit into each category.

Conductors: Gold, Iron, Silver, Copper, Aluminum, Tin
Semiconductors: Silicon, Germanium
Insulators: Glass, Porcelain, Rubber, Cloth, Paper, Air

[[File:NatCopper.png|200px|thumb|left|Copper Conductor]]
[[File:Semiconductor-1.jpg|200px|thumb|left|Semiconductors]]
[[File:Rubber_band.jpg|200px|thumb|left|Rubber Insulator]]
[[File:plasma-ball-2282449_960_720.jpg|200px|thumb|left|Plasma]]

==Conductivity By Material Type==

===Metals===

Conductivity in metals decreases when temperature is increased. When the temperature increases, the resistance of the metal also increases linearly. As the temperature of a metal is reduced, the temperature dependence of resistivity follows a power law function of temperature.

The structure of metal is made up of a lattice of atoms. The outer shell of electrons that surround the parent atoms can come free and travel throughout the lattice, also known as an positive ionic lattice. A simpler definition of this phenomenon is the "sea" of electrons. This "sea" of electrons can move throughout the metal structure and conduct an electrical current. The electric field created by the electric potential cause the electrons to move to the positive terminal. The electrons are packed so densely that the electromagnetic field can travel at the speed of light with each electron having a small drift velocity.

The resistance in metals are created by temperature, the cross sectional area, the length, and the speed of vibration of the crystal lattice. The more resistance that is present the less conductive the metal is. The temperature causes irregularities in the lattice. If the cross sectional area is bigger then there is more electrons per unit length are available to carry current. Therefore, the smaller the cross sectional area the more resistance in the wire. The longer the wire the more likely scattering events take place. The more scattering events the higher the resistance in the wire. Impurities in the metal increase resistance too. The different ions in the metal create irregularities, which in turn create a vibration in the metal.

=== Semiconductors ===

Semiconductors are materials that have a conductivity in-between that of an insulator and a conductor. Their electrical resistance are much higher than ordinary conductors but still much lower than most insulators. Interestingly enough, their resistance decreases as their temperature increases, which is behavior opposite to that of a metal (insulator).

==== Temperature Dependence ====

Conductivity of a material is determined by two factors: the concentration of free carriers available
to conduct current and their mobility (or freedom to move). In a semiconductor, both mobility and
carrier concentration are temperature dependent.
As temperature increases, the electrical resistivity of metals increases. This is a reason why when computers heat up, they tend to slow down. Some materials exhibit superconductivity at extremely low temperatures. Below a certain temperature, resistivity vanishes, such as Pb (Lead) at 7.20 K.

===Plasma===

Plasma is a very good electrical conductor. Its electric potential is a special potential called plasma or space potential. It exists in the space between charged particles. If an electrode was put inside the plasma the potential would drop a considerable amount compared to the plasma potential because of a phenomenon called Debye sheath. The high conductivity results in relatively small electric fields.

==Band Theory==

==Equations==

'''Conductivity Relationship to Resistivity'''

<math>σ=1/ρ</math>

σ= Conductivity
ρ= Electric Resistivity

'''Maxwell's Equation for Electric Conductivity'''

<math>J=σE</math>

J= Electric Current Density
E= Electric Field
σ= Conductivity

Electric current density can be thought of as the electric current per cross sectional area of a specific material. Therefore this formula relates to each material differently. Every material has a specific conductivity associated with it, and this conductivity can help describe the electric field in each material. For example, materials such as copper and silver have extremely high electric conductivity and therefore in order to not have an almost infinite electric current density we can approximate the electric field inside the metals to be zero. This equation is essentially the proof for all metals having a zero electric field on the inside. The relationship between these three variables is known as Ohm's Law.

'''Poulliet's Law of Resistivity'''[[File:Resistivity_geometry.png|220px|thumb|right|Section of resistive material with a cross section and length.]]

<math>R=ρℓ/A </math>

R = Electric Resistance
ρ = Electric Resistivity
ℓ = Length
A = Cross-Sectional Area

Poulliet's Law states that a given material's resistance will increase in length, while it will decrease with an increase in Area. The SI unit for this law is Ohm*meter. The electrical resistivity is different for every substance.

==Conductivity in Real Life==

Conductors are used to carry electricity, as well as electrical signals in circuits.
Complementary metal–oxide–semiconductors, or CMOS for short, are the foundational building block of gate based logic circuits, that make up the majority of all modern electronics. CMOS circuits are composed of a combination of p-type and n-type semiconductors. These semiconductors will change their conductivity, based on the applied voltage, allowing for logic of 0's and 1's, or low voltage and high voltage, to be transferred through logical circuits. This allows us to apply boolean logic to circuits, such as AND and OR logic, or even create an amalgamation of AND's and OR's to create electronics, such as multiplexors, switches, latches, registers, decoders, encoders, etc.

=== Fun Examples ===
[https://www.youtube.com/watch?v=ODbgKXFED5o Salt Water Conductivity Experiment]

[https://www.youtube.com/watch?v=HaQnlftxQUU Fruit Conductivity Experiment]

===Mathematical Problems===
====Simple====
Find the Conductivity of a material with an electrical field of <math>5*10^{12} (E = 5*10^{12})</math> and a current density of <math>5*10^2
(J = 5*10^2)</math>.
{| class="wikitable mw-collapsible mw-collapsed"
! Answer
|-
| <math> =10^{10} </math>
|}

====Medium====
Find the Resistivity of a wire with the resistance of <math>0.69Ω*m (R=0.69Ω*m)</math>, length of <math>10m (ℓ=10m)</math>, and cross-sectional area of <math>100m^{2} (A=100m^{2})</math>.
{| class="wikitable mw-collapsible mw-collapsed"
! Answer
|-
| 690 = 10ρ
|-
| ρ = 69
|}

==History==
'''Stephen Gray, Father of Conduction'''

''Born 1666 in Canterbury, England.''
''Died 1736 in London, England.''

Gray was an innovative thinker who performed many a experiment including work with the transmission of electricity. One day while performing one of his experiments, unbeknownst to him he discovered the difference between insulators and conductors. He was working with transmitting electricity and he changed the transmission wire from silk to brass wire when he noticed that electricity passes completely different in brass than it does in silk. After said discovery, Gray spend the next 3 years with the help of friends and family doing more research in similar topics, and with this research some might say solidified his name as the father of conduction.

'''Claude Pouillet, Pouillet's Law'''

''Born February 16, 1720 in Cusance, France.''
''Died June 14, 1868 in Paris, France.''

Claude was one of the earliest scientists to examine the Sun's influence on Earth's atmosphere, beyond simple radiation. After approximating the solar constant to be 1228 <math> W/m^{2} </math>, which turned out to be extremely close to the now recognized constant of 1367 <math> W/m^{2} </math>. This success earned him a chair in the Physics department at the École Normale Supérieure. From there he went on to design and create early, operational versions of sine and tangent galvanometers which measure current (more commonly known as an ammeter).

===Further reading===

[http://www.mse.gatech.edu/research/equipment-facilities/electrical-properties-materials-and-devices Georgia Tech Research and Information regarding conduction in School of Materials Science and Engineering]

[http://hyperphysics.phy-astr.gsu.edu/hbase/electric/resis.html HyperPhysics Explanations]

===External links===
[http://www.physics4kids.com/files/elec_conduct.html Beginner Explanation]

[http://formulas.tutorvista.com/physics/thermal-conductivity-formula.html Thermal Conductivity]

[http://britneyspears.ac/physics/basics/basics.htm Brittany Spears explains semiconductors]

Conductivity

2017-11-29T20:37:23Z

Achawki3: /* Equations */

Claimed by Patrick Todd (Spring 2017) Claimed by Anthony Chawki (Fall 2017)

'''
==Definition==
'''Conductivity''' is the degree to which a specified material conducts electricity, calculated as the ratio of the current density in the material to the electric field that causes the flow of current. (It is the ''reciprocal'' of the resistivity.)

In other words, Conductivity is the measure of the ease at which an electric charge or heat can pass through a material.
'''Electrical conductivity''' tells us how well a material will allow electricity to travel through it.
'''Thermal conductivity''' tells us the ease upon which thermal energy (heat for most purposes) can move through a material.

==Symbols==

Electrical Conductivity is measured in siemens per meter and is often represented using the Greek letters '''σ''' (lowercase sigma), '''κ''' (kappa), or '''γ''' (lowercase gamma).

== SI Units ==

Conductivity's SI units is the siemens per metre, <math> A^{2} s^{3} m^{−3} kg^{−1} </math>(named after Werner von Siemens) or, more simply, <math>S m^{−1}</math>.

== Classification of Materials by Conductivity ==

Conductors, Semiconductors, and Insulators are the main three classifications of a material when talking about its electrical conductivity. Conductors are materials with high conductivity. Semiconductors have an in between level of conductivity, while insulators have low conductivity. Meaning if you want to pass a lot of electricity to something use a conductor, if you want to pass some electricity but also lower the original amount use a semiconductor, and if you want to cut the flow of electricity use an insulator. Provided below is a list of materials that fit into each category.

Conductors: Gold, Iron, Silver, Copper, Aluminum, Tin
Semiconductors: Silicon, Germanium
Insulators: Glass, Porcelain, Rubber, Cloth, Paper, Air

[[File:NatCopper.png|200px|thumb|left|Copper Conductor]][[File:Semiconductor-1.jpg|200px|thumb|center|Semiconductors]][[File:Rubber_band.jpg|200px|thumb|right|Rubber Insulator]]

==Conductivity By Material Phase==

===Metals===

Conductivity in metals decreases when temperature is increased. When the temperature increases, the resistance of the metal also increases linearly. As the temperature of a metal is reduced, the temperature dependence of resistivity follows a power law function of temperature.

=== Semiconductors ===

Semiconductors are materials that have a conductivity in-between that of an insulator and a conductor. Their electrical resistance are much higher than ordinary conductors but still much lower than most insulators. Interestingly enough, their resistance decreases as their temperature increases, which is behavior opposite to that of a metal (insulator).

==== Temperature Dependence ====

Conductivity of a material is determined by two factors: the concentration of free carriers available
to conduct current and their mobility (or freedom to move). In a semiconductor, both mobility and
carrier concentration are temperature dependent.
As temperature increases, the electrical resistivity of metals increases. This is a reason why when computers heat up, they tend to slow down. Some materials exhibit superconductivity at extremely low temperatures. Below a certain temperature, resistivity vanishes, such as Pb (Lead) at 7.20 K.

====Band Theory====

===Plasma===

==Equations==

'''Conductivity Relationship to Resistivity'''

<math>σ=1/ρ</math>

σ= Conductivity
ρ= Electric Resistivity

'''Maxwell's Equation for Electric Conductivity'''

<math>J=σE</math>

J= Electric Current Density
E= Electric Field
σ= Conductivity

Electric current density can be thought of as the electric current per cross sectional area of a specific material. Therefore this formula relates to each material differently. Every material has a specific conductivity associated with it, and this conductivity can help describe the electric field in each material. For example, materials such as copper and silver have extremely high electric conductivity and therefore in order to not have an almost infinite electric current density we can approximate the electric field inside the metals to be zero. This equation is essentially the proof for all metals having a zero electric field on the inside. The relationship between these three variables is known as Ohm's Law.

'''Poulliet's Law of Resistivity'''[[File:Resistivity_geometry.png|220px|thumb|right|Section of resistive material with a cross section and length.]]

<math>R=ρℓ/A </math>

R = Electric Resistance
ρ = Electric Resistivity
ℓ = Length
A = Cross-Sectional Area

Poulliet's Law states that a given material's resistance will increase in length, while it will decrease with an increase in Area. The SI unit for this law is Ohm*meter. The electrical resistivity is different for every substance.

==Conductivity in Real Life==

Conductors are used to carry electricity, as well as electrical signals in circuits.
Complementary metal–oxide–semiconductors, or CMOS for short, are the foundational building block of gate based logic circuits, that make up the majority of all modern electronics. CMOS circuits are composed of a combination of p-type and n-type semiconductors. These semiconductors will change their conductivity, based on the applied voltage, allowing for logic of 0's and 1's, or low voltage and high voltage, to be transferred through logical circuits. This allows us to apply boolean logic to circuits, such as AND and OR logic, or even create an amalgamation of AND's and OR's to create electronics, such as multiplexors, switches, latches, registers, decoders, encoders, etc.

=== Fun Examples ===
[https://www.youtube.com/watch?v=ODbgKXFED5o Salt Water Conductivity Experiment]

[https://www.youtube.com/watch?v=HaQnlftxQUU Fruit Conductivity Experiment]

===Mathematical Problems===
====Simple====
Find the Conductivity of a material with an electrical field of <math>5*10^{12} (E = 5*10^{12})</math> and a current density of <math>5*10^2
(J = 5*10^2)</math>.
{| class="wikitable mw-collapsible mw-collapsed"
! Answer
|-
| <math> =10^{10} </math>
|}

====Medium====
Find the Resistivity of a wire with the resistance of <math>0.69Ω*m (R=0.69Ω*m)</math>, length of <math>10m (ℓ=10m)</math>, and cross-sectional area of <math>100m^{2} (A=100m^{2})</math>.
{| class="wikitable mw-collapsible mw-collapsed"
! Answer
|-
| 690 = 10ρ
|-
| ρ = 69
|}

==History==
'''Stephen Gray, Father of Conduction'''

''Born 1666 in Canterbury, England.''
''Died 1736 in London, England.''

Gray was an innovative thinker who performed many a experiment including work with the transmission of electricity. One day while performing one of his experiments, unbeknownst to him he discovered the difference between insulators and conductors. He was working with transmitting electricity and he changed the transmission wire from silk to brass wire when he noticed that electricity passes completely different in brass than it does in silk. After said discovery, Gray spend the next 3 years with the help of friends and family doing more research in similar topics, and with this research some might say solidified his name as the father of conduction.

'''Claude Pouillet, Pouillet's Law'''

''Born February 16, 1720 in Cusance, France.''
''Died June 14, 1868 in Paris, France.''

Claude was one of the earliest scientists to examine the Sun's influence on Earth's atmosphere, beyond simple radiation. After approximating the solar constant to be 1228 <math> W/m^{2} </math>, which turned out to be extremely close to the now recognized constant of 1367 <math> W/m^{2} </math>. This success earned him a chair in the Physics department at the École Normale Supérieure. From there he went on to design and create early, operational versions of sine and tangent galvanometers which measure current (more commonly known as an ammeter).

===Further reading===

[http://www.mse.gatech.edu/research/equipment-facilities/electrical-properties-materials-and-devices Georgia Tech Research and Information regarding conduction in School of Materials Science and Engineering]

[http://hyperphysics.phy-astr.gsu.edu/hbase/electric/resis.html HyperPhysics Explanations]

===External links===
[http://www.physics4kids.com/files/elec_conduct.html Beginner Explanation]

[http://formulas.tutorvista.com/physics/thermal-conductivity-formula.html Thermal Conductivity]

[http://britneyspears.ac/physics/basics/basics.htm Brittany Spears explains semiconductors]

Conductivity

2017-11-29T05:06:19Z

Speed of Sound in Solids

2016-11-28T02:44:33Z

Achawki3: /* The Main Idea */

CLAIMED BY ANTHONY CHAWKI
This page discusses calculating the speed of sound in various solids and provides examples of such calculations.

==The Main Idea==

The speed of sound is the speed that sound waves travel through a particular medium. The medium determines the speed limit. [[File:2743324.png|right|border]]Mediums are composed of particles that could be closely knit together or relatively spread apart. Also, these particles could act elastic or inelastic. The closer together the particles are to each other the faster the sound can be transferred through the medium. In comparison to air, sound travels considerably faster in solids. The factors that control the speed that sound travels in various solids is measured by the solid's density and elasticity, as these factors effect the vibrational energy of the sound.

With an increase in density, the space between particles in the solid decreases. The smaller distance between particles, or interatomic distance, the higher the speed. With an increase in elasticity of the atoms that make up the object, the lower the speed of sound in the object. Particles that have a high elasticity take more time to return to their place once they received vibrational energy. However, if the solid is completely inelastic then the sound cannot travel through it.

The practicality of this concept is great. Everyday humans' ears capture sound waves through the Pinna, [[File:Blausen_0330_EarAnatomy_MiddleEar.png|thumb|border|right|baseline|The inner ear.]]or the outer cartilage piece of the ear. The sound waves then travel up the ear canal and hit the ear drum, which vibrates from the sound. The vibrations travel through the inner ear and end up at the Cochlea. The Cochlea transfers the vibrations into information that the auditory nerve can analyze. This process occurs everyday and without proper education of sound traveling through solids, such as the ear's different pieces, humans wouldn't be able to completely understand the concept completely.

===A Mathematical Model===

The speed of sound in solids <math> {V_{s}} </math> can be determined by the equation. Young's Modulus is a measure of elasticity of an object, and it can be computed to solve for interatomic values, such as interatomic bond stiffness or interatomic bond length.

<math> {V_{s}} = d* √ (K_{s}/m_{atom}) </math>

Alternative speed equation:

<math> {V_{s}} = √ (B/ρ) </math>

<math> ρ </math> = density

<math> B </math> = Bulks Modulus

Bulks Modulus = <math>{\frac {ΔP}{ΔV/V}} </math>
[[File:bulk3.gif|border|right|middle]]
<math> d </math> = interatomic bond length

<math> K_{s} </math> = Interatomic bond stiffness

Youngs Modulus = (<math> Y = K_{s}/d </math>)

Youngs Modulus: <math> Y ={\frac{Stress}{Strain}}</math>

<math> Stress = {\frac{F_{tension}}{Area_{Cross Sectional}}} </math>

<math> Strain = {\frac{ΔL_{wire}}{L_{0}}} </math>

===Speeds of Various Compositions===
[[File:speedofsound.jpg]]

==Examples==

===Theoretical===

Two metal rods are made of different elements. The interatomic spring stiffness of element A is four times larger than the interatomic spring stiffness for element B. The mass of an atom of element A is four times greater than the mass of an atom of element B. The atomic diameters are approximately the same for A and B. What is the ratio of the speed of sound in rod A to the speed of sound in rod B?

Solution: In this situation, the ratio of the speed of sound in rod A to the speed of sound in rod B is 1.

Looking at the formula for computing speed of sound in solids, <math> {V_{s}} = d* √ (K_{s}/m_{atom}) </math>, you see that velocity depends three factors, interatomic stiffness, the mass of one atom, and interatomic bond length. The two rods differences in atomic mass and interatomic stiffness offset each other when the equations are set equal, and the ratio is determined to be 1.

<math> d* √ 4(K_{s}/m_{atom}) = d* √ (K_{s}/4m_{atom}) </math> After simplification <math> V_{s_{1}} = V_{s{2}} </math>

===Numerical Example ===
The Young's Modulus value of silver is 7.75e+10, atomic mass of silver is 108 g/mole, and the density of silver is 10.5 g/cm3. Using this information, calculate the speed of sound in silver.

Solution: The key to solving this problem is to realize the micro-macro connection of Young's Modulus. You are given that Young's Modulus is equal to 7.75e+10, and we know that
Youngs Modulus = (<math> K_{s}/d </math>). In this situation, we need to calculate the interatomic bond length and use it and our Young's Modulus value to determine our interatomic stiffness.

To solve for ''d'', we use the given density of silver (10.5 g/cm3). Using the basic equation for volume in relation to density and mass (<math> V=m*d</math>), we can find ''d'', since ''d'' is equal to the cube root of volume.

Once ''d'' is solved for, it can be plugged back into the the equation <math> Y = K_{s}/d </math> to solve for <math> K_{s} </math>

Now, we have solved for both interatomic bond length and stiffness. The only quantity in the final speed of sound equation we need is the mass of one atom, which can be determined using Avogardro's number and the atomic mass. <math> m_{atom} = </math> ''atomic mass'' / <math> 6.022e23 </math>

Now that all variables are solved for, we can substitute values into our <math> {V_{s}} = d* √ (K_{s}/m_{atom}) </math> equation.

<math> {V_{s}} = 1.6e-10* √ (78534.7/1.79e-22) </math>

<math> {V_{s}} = 2723</math> m/s

==Connectedness==
The computation of speed of sound in solids is dependent on a mass' interatomic properties, such as interatomic bond length. I find it interesting when a object's interatomic properties determine its functionality on a larger scale. In the case of speed of sound in solids, the objects elasticity depends on the interatomic bond length.

While the computation of speed of sound in solids may not seem related to Industrial Engineering, it has clear implications in the process of choosing building materials, which is a notable section of industrial engineering. For example, if you are planning to build something soundproof, it would be optimal to choose a solid with a very low speed of sound velocity.

The industrial applications in terms of construction are vast. An objects ability to block/allow sound waves through it is very important. Of course, insulation materials and sound proof wall materials come to thought at first. However, in some cases, contractors need to build structures that allow sound to travel through, in which they would choose solid materials that correlate with high speeds of sound.

==History==

The speed of sound in air was first measured by Sir Isaac Newton, and first correctly computed by Pierre-Simon Laplace in 1816. Before this precise measurement, attempts had been made across Europe during the 1700s, most famously Reverend William Derham's experiment in 1709 across the town of Upminister, England. Reverend Derham used a shotgun's noise and several known landmarks around time to measure the time it took for the sound of the blast to be heard from select distances.

Young's Modulus was named after English physicist Thomas Young. In actuality, the concept was developed earlier by physicists Leonhard Euler and Giordano Riccati in the 1720s.

== See also ==

Youngs Modulus: [http://www.physicsbook.gatech.edu/Young%27s_Modulus]
Interatomic Bonds: [http://www.physicsbook.gatech.edu/Length_and_Stiffness_of_an_Interatomic_Bond]

===Further reading===

Further Information can be found on the speed of sound in solids in ''Matter and Interactions, 4th Edition'' by Ruth W. Chabay & Bruce A. Sherwood
===External links===

Internet resources on this topic can be found at:

Engineering Tool Box [http://www.engineeringtoolbox.com/sound-speed-solids-d_713.html]

Hyperphysics [http://hyperphysics.phy-astr.gsu.edu/hbase/sound/souspe2.html]

Potto Project [http://www.potto.org/gasDynamics/node73.html]

NDT Resource Center [https://www.nde-ed.org/EducationResources/CommunityCollege/Ultrasonics/Physics/elasticsolids.htm]

The Engineering ToolBox [http://www.engineeringtoolbox.com/speed-sound-d_82.html]

Ear Image [https://commons.wikimedia.org/wiki/File:Blausen_0330_EarAnatomy_MiddleEar.png]

Yew Chung [http://ycis-sir.weebly.com/gigamind-a-sound-experience.html]

==References==

This section contains the the references used while writing this page

Chart from [http://www.rcgroups.com/forums/attachment.php?attachmentid=3397792]

''Matter and Interactions 4th Edition'' by Chabay and Sherwood

Wikipage created by Daiven Patel

File:2743324.png

2016-11-28T02:32:17Z

Achawki3:

Speed of Sound in Solids

2016-11-28T01:58:45Z

Achawki3: /* A Mathematical Model */

CLAIMED BY ANTHONY CHAWKI
This page discusses calculating the speed of sound in various solids and provides examples of such calculations.

==The Main Idea==

The speed of sound is the speed that sound waves travel through a particular medium. The medium determines the speed limit. Mediums are composed of particles that could be closely knit together or relatively spread apart. Also, these particles could act elastic or inelastic. The closer together the particles are to each other the faster the sound can be transferred through the medium. In comparison to air, sound travels considerably faster in solids. The factors that control the speed that sound travels in various solids is measured by the solid's density and elasticity, as these factors effect the vibrational energy of the sound.

With an increase in density, the space between particles in the solid decreases. The smaller distance between particles, or interatomic distance, the higher the speed. With an increase in elasticity of the atoms that make up the object, the lower the speed of sound in the object. Particles that have a high elasticity take more time to return to their place once they received vibrational energy. However, if the solid is completely inelastic then the sound cannot travel through it.

The practicality of this concept is great. Everyday humans' ears capture sound waves through the Pinna, [[File:Blausen_0330_EarAnatomy_MiddleEar.png|thumb|border|right|baseline|The inner ear.]]or the outer cartilage piece of the ear. The sound waves then travel up the ear canal and hit the ear drum, which vibrates from the sound. The vibrations travel through the inner ear and end up at the Cochlea. The Cochlea transfers the vibrations into information that the auditory nerve can analyze. This process occurs everyday and without proper education of sound traveling through solids, such as the ear's different pieces, humans wouldn't be able to completely understand the concept completely.

===A Mathematical Model===

The speed of sound in solids <math> {V_{s}} </math> can be determined by the equation. Young's Modulus is a measure of elasticity of an object, and it can be computed to solve for interatomic values, such as interatomic bond stiffness or interatomic bond length.

<math> {V_{s}} = d* √ (K_{s}/m_{atom}) </math>

Alternative speed equation:

<math> {V_{s}} = √ (B/ρ) </math>

<math> ρ </math> = density

<math> B </math> = Bulks Modulus

Bulks Modulus = <math>{\frac {ΔP}{ΔV/V}} </math>
[[File:bulk3.gif|border|right|middle]]
<math> d </math> = interatomic bond length

<math> K_{s} </math> = Interatomic bond stiffness

Youngs Modulus = (<math> Y = K_{s}/d </math>)

Youngs Modulus: <math> Y ={\frac{Stress}{Strain}}</math>

<math> Stress = {\frac{F_{tension}}{Area_{Cross Sectional}}} </math>

<math> Strain = {\frac{ΔL_{wire}}{L_{0}}} </math>

===Speeds of Various Compositions===
[[File:speedofsound.jpg]]

==Examples==

===Theoretical===

Two metal rods are made of different elements. The interatomic spring stiffness of element A is four times larger than the interatomic spring stiffness for element B. The mass of an atom of element A is four times greater than the mass of an atom of element B. The atomic diameters are approximately the same for A and B. What is the ratio of the speed of sound in rod A to the speed of sound in rod B?

Solution: In this situation, the ratio of the speed of sound in rod A to the speed of sound in rod B is 1.

Looking at the formula for computing speed of sound in solids, <math> {V_{s}} = d* √ (K_{s}/m_{atom}) </math>, you see that velocity depends three factors, interatomic stiffness, the mass of one atom, and interatomic bond length. The two rods differences in atomic mass and interatomic stiffness offset each other when the equations are set equal, and the ratio is determined to be 1.

<math> d* √ 4(K_{s}/m_{atom}) = d* √ (K_{s}/4m_{atom}) </math> After simplification <math> V_{s_{1}} = V_{s{2}} </math>

===Numerical Example ===
The Young's Modulus value of silver is 7.75e+10, atomic mass of silver is 108 g/mole, and the density of silver is 10.5 g/cm3. Using this information, calculate the speed of sound in silver.

Solution: The key to solving this problem is to realize the micro-macro connection of Young's Modulus. You are given that Young's Modulus is equal to 7.75e+10, and we know that
Youngs Modulus = (<math> K_{s}/d </math>). In this situation, we need to calculate the interatomic bond length and use it and our Young's Modulus value to determine our interatomic stiffness.

To solve for ''d'', we use the given density of silver (10.5 g/cm3). Using the basic equation for volume in relation to density and mass (<math> V=m*d</math>), we can find ''d'', since ''d'' is equal to the cube root of volume.

Once ''d'' is solved for, it can be plugged back into the the equation <math> Y = K_{s}/d </math> to solve for <math> K_{s} </math>

Now, we have solved for both interatomic bond length and stiffness. The only quantity in the final speed of sound equation we need is the mass of one atom, which can be determined using Avogardro's number and the atomic mass. <math> m_{atom} = </math> ''atomic mass'' / <math> 6.022e23 </math>

Now that all variables are solved for, we can substitute values into our <math> {V_{s}} = d* √ (K_{s}/m_{atom}) </math> equation.

<math> {V_{s}} = 1.6e-10* √ (78534.7/1.79e-22) </math>

<math> {V_{s}} = 2723</math> m/s

==Connectedness==
The computation of speed of sound in solids is dependent on a mass' interatomic properties, such as interatomic bond length. I find it interesting when a object's interatomic properties determine its functionality on a larger scale. In the case of speed of sound in solids, the objects elasticity depends on the interatomic bond length.

While the computation of speed of sound in solids may not seem related to Industrial Engineering, it has clear implications in the process of choosing building materials, which is a notable section of industrial engineering. For example, if you are planning to build something soundproof, it would be optimal to choose a solid with a very low speed of sound velocity.

The industrial applications in terms of construction are vast. An objects ability to block/allow sound waves through it is very important. Of course, insulation materials and sound proof wall materials come to thought at first. However, in some cases, contractors need to build structures that allow sound to travel through, in which they would choose solid materials that correlate with high speeds of sound.

==History==

The speed of sound in air was first measured by Sir Isaac Newton, and first correctly computed by Pierre-Simon Laplace in 1816. Before this precise measurement, attempts had been made across Europe during the 1700s, most famously Reverend William Derham's experiment in 1709 across the town of Upminister, England. Reverend Derham used a shotgun's noise and several known landmarks around time to measure the time it took for the sound of the blast to be heard from select distances.

Young's Modulus was named after English physicist Thomas Young. In actuality, the concept was developed earlier by physicists Leonhard Euler and Giordano Riccati in the 1720s.

== See also ==

Youngs Modulus: [http://www.physicsbook.gatech.edu/Young%27s_Modulus]
Interatomic Bonds: [http://www.physicsbook.gatech.edu/Length_and_Stiffness_of_an_Interatomic_Bond]

===Further reading===

Further Information can be found on the speed of sound in solids in ''Matter and Interactions, 4th Edition'' by Ruth W. Chabay & Bruce A. Sherwood
===External links===

Internet resources on this topic can be found at:

Engineering Tool Box [http://www.engineeringtoolbox.com/sound-speed-solids-d_713.html]

Hyperphysics [http://hyperphysics.phy-astr.gsu.edu/hbase/sound/souspe2.html]

Potto Project [http://www.potto.org/gasDynamics/node73.html]

NDT Resource Center [https://www.nde-ed.org/EducationResources/CommunityCollege/Ultrasonics/Physics/elasticsolids.htm]

The Engineering ToolBox [http://www.engineeringtoolbox.com/speed-sound-d_82.html]

Ear Image [https://commons.wikimedia.org/wiki/File:Blausen_0330_EarAnatomy_MiddleEar.png]

Yew Chung [http://ycis-sir.weebly.com/gigamind-a-sound-experience.html]

==References==

This section contains the the references used while writing this page

Chart from [http://www.rcgroups.com/forums/attachment.php?attachmentid=3397792]

''Matter and Interactions 4th Edition'' by Chabay and Sherwood

Wikipage created by Daiven Patel

Speed of Sound in Solids

2016-11-28T01:56:07Z

Achawki3: /* The Main Idea */

CLAIMED BY ANTHONY CHAWKI
This page discusses calculating the speed of sound in various solids and provides examples of such calculations.

==The Main Idea==

The speed of sound is the speed that sound waves travel through a particular medium. The medium determines the speed limit. Mediums are composed of particles that could be closely knit together or relatively spread apart. Also, these particles could act elastic or inelastic. The closer together the particles are to each other the faster the sound can be transferred through the medium. In comparison to air, sound travels considerably faster in solids. The factors that control the speed that sound travels in various solids is measured by the solid's density and elasticity, as these factors effect the vibrational energy of the sound.

With an increase in density, the space between particles in the solid decreases. The smaller distance between particles, or interatomic distance, the higher the speed. With an increase in elasticity of the atoms that make up the object, the lower the speed of sound in the object. Particles that have a high elasticity take more time to return to their place once they received vibrational energy. However, if the solid is completely inelastic then the sound cannot travel through it.

The practicality of this concept is great. Everyday humans' ears capture sound waves through the Pinna, [[File:Blausen_0330_EarAnatomy_MiddleEar.png|thumb|border|right|baseline|The inner ear.]]or the outer cartilage piece of the ear. The sound waves then travel up the ear canal and hit the ear drum, which vibrates from the sound. The vibrations travel through the inner ear and end up at the Cochlea. The Cochlea transfers the vibrations into information that the auditory nerve can analyze. This process occurs everyday and without proper education of sound traveling through solids, such as the ear's different pieces, humans wouldn't be able to completely understand the concept completely.

===A Mathematical Model===

The speed of sound in solids <math> {V_{s}} </math> can be determined by the equation. Young's Modulus is a measure of elasticity of an object, and it can be computed to solve for interatomic values, such as interatomic bond stiffness or interatomic bond length.

<math> {V_{s}} = d* √ (K_{s}/m_{atom}) </math>

Alternative speed equation:

<math> {V_{s}} = √ (B/ρ) </math>

<math> ρ </math> = density

<math> B </math> = Bulks Modulus

Bulks Modulus = <math>{\frac {ΔP}{ΔV/V}} </math>

<math> d </math> = interatomic bond length

<math> K_{s} </math> = Interatomic bond stiffness

Youngs Modulus = (<math> Y = K_{s}/d </math>)

Youngs Modulus: <math> Y ={\frac{Stress}{Strain}}</math>

<math> Stress = {\frac{F_{tension}}{Area_{Cross Sectional}}} </math>

<math> Strain = {\frac{ΔL_{wire}}{L_{0}}} </math>

===Speeds of Various Compositions===
[[File:speedofsound.jpg]]

==Examples==

===Theoretical===

Two metal rods are made of different elements. The interatomic spring stiffness of element A is four times larger than the interatomic spring stiffness for element B. The mass of an atom of element A is four times greater than the mass of an atom of element B. The atomic diameters are approximately the same for A and B. What is the ratio of the speed of sound in rod A to the speed of sound in rod B?

Solution: In this situation, the ratio of the speed of sound in rod A to the speed of sound in rod B is 1.

Looking at the formula for computing speed of sound in solids, <math> {V_{s}} = d* √ (K_{s}/m_{atom}) </math>, you see that velocity depends three factors, interatomic stiffness, the mass of one atom, and interatomic bond length. The two rods differences in atomic mass and interatomic stiffness offset each other when the equations are set equal, and the ratio is determined to be 1.

<math> d* √ 4(K_{s}/m_{atom}) = d* √ (K_{s}/4m_{atom}) </math> After simplification <math> V_{s_{1}} = V_{s{2}} </math>

===Numerical Example ===
The Young's Modulus value of silver is 7.75e+10, atomic mass of silver is 108 g/mole, and the density of silver is 10.5 g/cm3. Using this information, calculate the speed of sound in silver.

Solution: The key to solving this problem is to realize the micro-macro connection of Young's Modulus. You are given that Young's Modulus is equal to 7.75e+10, and we know that
Youngs Modulus = (<math> K_{s}/d </math>). In this situation, we need to calculate the interatomic bond length and use it and our Young's Modulus value to determine our interatomic stiffness.

To solve for ''d'', we use the given density of silver (10.5 g/cm3). Using the basic equation for volume in relation to density and mass (<math> V=m*d</math>), we can find ''d'', since ''d'' is equal to the cube root of volume.

Once ''d'' is solved for, it can be plugged back into the the equation <math> Y = K_{s}/d </math> to solve for <math> K_{s} </math>

Now, we have solved for both interatomic bond length and stiffness. The only quantity in the final speed of sound equation we need is the mass of one atom, which can be determined using Avogardro's number and the atomic mass. <math> m_{atom} = </math> ''atomic mass'' / <math> 6.022e23 </math>

Now that all variables are solved for, we can substitute values into our <math> {V_{s}} = d* √ (K_{s}/m_{atom}) </math> equation.

<math> {V_{s}} = 1.6e-10* √ (78534.7/1.79e-22) </math>

<math> {V_{s}} = 2723</math> m/s

==Connectedness==
The computation of speed of sound in solids is dependent on a mass' interatomic properties, such as interatomic bond length. I find it interesting when a object's interatomic properties determine its functionality on a larger scale. In the case of speed of sound in solids, the objects elasticity depends on the interatomic bond length.

While the computation of speed of sound in solids may not seem related to Industrial Engineering, it has clear implications in the process of choosing building materials, which is a notable section of industrial engineering. For example, if you are planning to build something soundproof, it would be optimal to choose a solid with a very low speed of sound velocity.

The industrial applications in terms of construction are vast. An objects ability to block/allow sound waves through it is very important. Of course, insulation materials and sound proof wall materials come to thought at first. However, in some cases, contractors need to build structures that allow sound to travel through, in which they would choose solid materials that correlate with high speeds of sound.

==History==

The speed of sound in air was first measured by Sir Isaac Newton, and first correctly computed by Pierre-Simon Laplace in 1816. Before this precise measurement, attempts had been made across Europe during the 1700s, most famously Reverend William Derham's experiment in 1709 across the town of Upminister, England. Reverend Derham used a shotgun's noise and several known landmarks around time to measure the time it took for the sound of the blast to be heard from select distances.

Young's Modulus was named after English physicist Thomas Young. In actuality, the concept was developed earlier by physicists Leonhard Euler and Giordano Riccati in the 1720s.

== See also ==

Youngs Modulus: [http://www.physicsbook.gatech.edu/Young%27s_Modulus]
Interatomic Bonds: [http://www.physicsbook.gatech.edu/Length_and_Stiffness_of_an_Interatomic_Bond]

===Further reading===

Further Information can be found on the speed of sound in solids in ''Matter and Interactions, 4th Edition'' by Ruth W. Chabay & Bruce A. Sherwood
===External links===

Internet resources on this topic can be found at:

Engineering Tool Box [http://www.engineeringtoolbox.com/sound-speed-solids-d_713.html]

Hyperphysics [http://hyperphysics.phy-astr.gsu.edu/hbase/sound/souspe2.html]

Potto Project [http://www.potto.org/gasDynamics/node73.html]

NDT Resource Center [https://www.nde-ed.org/EducationResources/CommunityCollege/Ultrasonics/Physics/elasticsolids.htm]

The Engineering ToolBox [http://www.engineeringtoolbox.com/speed-sound-d_82.html]

Ear Image [https://commons.wikimedia.org/wiki/File:Blausen_0330_EarAnatomy_MiddleEar.png]

Yew Chung [http://ycis-sir.weebly.com/gigamind-a-sound-experience.html]

==References==

This section contains the the references used while writing this page

Chart from [http://www.rcgroups.com/forums/attachment.php?attachmentid=3397792]

''Matter and Interactions 4th Edition'' by Chabay and Sherwood

Wikipage created by Daiven Patel

Speed of Sound in Solids

2016-11-28T01:55:40Z

Achawki3: /* The Main Idea */

CLAIMED BY ANTHONY CHAWKI
This page discusses calculating the speed of sound in various solids and provides examples of such calculations.

==The Main Idea==

The speed of sound is the speed that sound waves travel through a particular medium. The medium determines the speed limit. Mediums are composed of particles that could be closely knit together or relatively spread apart. Also, these particles could act elastic or inelastic. The closer together the particles are to each other the faster the sound can be transferred through the medium. In comparison to air, sound travels considerably faster in solids. The factors that control the speed that sound travels in various solids is measured by the solid's density and elasticity, as these factors effect the vibrational energy of the sound.

With an increase in density, the space between particles in the solid decreases. The smaller distance between particles, or interatomic distance, the higher the speed. With an increase in elasticity of the atoms that make up the object, the lower the speed of sound in the object. Particles that have a high elasticity take more time to return to their place once they received vibrational energy. However, if the solid is completely inelastic then the sound cannot travel through it. [[File:bulk3.gif]]

The practicality of this concept is great. Everyday humans' ears capture sound waves through the Pinna, [[File:Blausen_0330_EarAnatomy_MiddleEar.png|thumb|border|right|baseline|The inner ear.]]or the outer cartilage piece of the ear. The sound waves then travel up the ear canal and hit the ear drum, which vibrates from the sound. The vibrations travel through the inner ear and end up at the Cochlea. The Cochlea transfers the vibrations into information that the auditory nerve can analyze. This process occurs everyday and without proper education of sound traveling through solids, such as the ear's different pieces, humans wouldn't be able to completely understand the concept completely.

===A Mathematical Model===

The speed of sound in solids <math> {V_{s}} </math> can be determined by the equation. Young's Modulus is a measure of elasticity of an object, and it can be computed to solve for interatomic values, such as interatomic bond stiffness or interatomic bond length.

<math> {V_{s}} = d* √ (K_{s}/m_{atom}) </math>

Alternative speed equation:

<math> {V_{s}} = √ (B/ρ) </math>

<math> ρ </math> = density

<math> B </math> = Bulks Modulus

Bulks Modulus = <math>{\frac {ΔP}{ΔV/V}} </math>

<math> d </math> = interatomic bond length

<math> K_{s} </math> = Interatomic bond stiffness

Youngs Modulus = (<math> Y = K_{s}/d </math>)

Youngs Modulus: <math> Y ={\frac{Stress}{Strain}}</math>

<math> Stress = {\frac{F_{tension}}{Area_{Cross Sectional}}} </math>

<math> Strain = {\frac{ΔL_{wire}}{L_{0}}} </math>

===Speeds of Various Compositions===
[[File:speedofsound.jpg]]

==Examples==

===Theoretical===

Two metal rods are made of different elements. The interatomic spring stiffness of element A is four times larger than the interatomic spring stiffness for element B. The mass of an atom of element A is four times greater than the mass of an atom of element B. The atomic diameters are approximately the same for A and B. What is the ratio of the speed of sound in rod A to the speed of sound in rod B?

Solution: In this situation, the ratio of the speed of sound in rod A to the speed of sound in rod B is 1.

Looking at the formula for computing speed of sound in solids, <math> {V_{s}} = d* √ (K_{s}/m_{atom}) </math>, you see that velocity depends three factors, interatomic stiffness, the mass of one atom, and interatomic bond length. The two rods differences in atomic mass and interatomic stiffness offset each other when the equations are set equal, and the ratio is determined to be 1.

<math> d* √ 4(K_{s}/m_{atom}) = d* √ (K_{s}/4m_{atom}) </math> After simplification <math> V_{s_{1}} = V_{s{2}} </math>

===Numerical Example ===
The Young's Modulus value of silver is 7.75e+10, atomic mass of silver is 108 g/mole, and the density of silver is 10.5 g/cm3. Using this information, calculate the speed of sound in silver.

Solution: The key to solving this problem is to realize the micro-macro connection of Young's Modulus. You are given that Young's Modulus is equal to 7.75e+10, and we know that
Youngs Modulus = (<math> K_{s}/d </math>). In this situation, we need to calculate the interatomic bond length and use it and our Young's Modulus value to determine our interatomic stiffness.

To solve for ''d'', we use the given density of silver (10.5 g/cm3). Using the basic equation for volume in relation to density and mass (<math> V=m*d</math>), we can find ''d'', since ''d'' is equal to the cube root of volume.

Once ''d'' is solved for, it can be plugged back into the the equation <math> Y = K_{s}/d </math> to solve for <math> K_{s} </math>

Now, we have solved for both interatomic bond length and stiffness. The only quantity in the final speed of sound equation we need is the mass of one atom, which can be determined using Avogardro's number and the atomic mass. <math> m_{atom} = </math> ''atomic mass'' / <math> 6.022e23 </math>

Now that all variables are solved for, we can substitute values into our <math> {V_{s}} = d* √ (K_{s}/m_{atom}) </math> equation.

<math> {V_{s}} = 1.6e-10* √ (78534.7/1.79e-22) </math>

<math> {V_{s}} = 2723</math> m/s

==Connectedness==
The computation of speed of sound in solids is dependent on a mass' interatomic properties, such as interatomic bond length. I find it interesting when a object's interatomic properties determine its functionality on a larger scale. In the case of speed of sound in solids, the objects elasticity depends on the interatomic bond length.

While the computation of speed of sound in solids may not seem related to Industrial Engineering, it has clear implications in the process of choosing building materials, which is a notable section of industrial engineering. For example, if you are planning to build something soundproof, it would be optimal to choose a solid with a very low speed of sound velocity.

The industrial applications in terms of construction are vast. An objects ability to block/allow sound waves through it is very important. Of course, insulation materials and sound proof wall materials come to thought at first. However, in some cases, contractors need to build structures that allow sound to travel through, in which they would choose solid materials that correlate with high speeds of sound.

==History==

The speed of sound in air was first measured by Sir Isaac Newton, and first correctly computed by Pierre-Simon Laplace in 1816. Before this precise measurement, attempts had been made across Europe during the 1700s, most famously Reverend William Derham's experiment in 1709 across the town of Upminister, England. Reverend Derham used a shotgun's noise and several known landmarks around time to measure the time it took for the sound of the blast to be heard from select distances.

Young's Modulus was named after English physicist Thomas Young. In actuality, the concept was developed earlier by physicists Leonhard Euler and Giordano Riccati in the 1720s.

== See also ==

Youngs Modulus: [http://www.physicsbook.gatech.edu/Young%27s_Modulus]
Interatomic Bonds: [http://www.physicsbook.gatech.edu/Length_and_Stiffness_of_an_Interatomic_Bond]

===Further reading===

Further Information can be found on the speed of sound in solids in ''Matter and Interactions, 4th Edition'' by Ruth W. Chabay & Bruce A. Sherwood
===External links===

Internet resources on this topic can be found at:

Engineering Tool Box [http://www.engineeringtoolbox.com/sound-speed-solids-d_713.html]

Hyperphysics [http://hyperphysics.phy-astr.gsu.edu/hbase/sound/souspe2.html]

Potto Project [http://www.potto.org/gasDynamics/node73.html]

NDT Resource Center [https://www.nde-ed.org/EducationResources/CommunityCollege/Ultrasonics/Physics/elasticsolids.htm]

The Engineering ToolBox [http://www.engineeringtoolbox.com/speed-sound-d_82.html]

Ear Image [https://commons.wikimedia.org/wiki/File:Blausen_0330_EarAnatomy_MiddleEar.png]

Yew Chung [http://ycis-sir.weebly.com/gigamind-a-sound-experience.html]

==References==

This section contains the the references used while writing this page

Chart from [http://www.rcgroups.com/forums/attachment.php?attachmentid=3397792]

''Matter and Interactions 4th Edition'' by Chabay and Sherwood

Wikipage created by Daiven Patel

2016-11-08T22:50:10Z

Achawki3:

CLAIMED BY ANTHONY CHAWKI
This page discusses calculating the speed of sound in various solids and provides examples of such calculations.

==The Main Idea==

The speed of sound is the speed that sound wave travels through a particular medium. In comparison to air, sound travels considerably faster in solids. The speed that sound travels in various solids depends on the solid's density and elasticity, as these factors effect the ability of the sound waves vibrational energy to transfer across the solid medium.

===A Mathematical Model===

The speed of sound in solids <math> {V_{s}} </math> can be determined by the equation. Young's Modulus is a measure of elasticity of an object, and it can be computed to solve for interatomic values, such as interatomic bond stiffness or interatomic bond length.

<math> {V_{s}} = d* √ (K_{s}/m_{atom}) </math>

<math> d </math> = interatomic bond length

<math> K_{s} </math> = Interatomic bond stiffness

Youngs Modulus = (<math> Y = K_{s}/d </math>)

Youngs Modulus: <math> Y ={\frac{Stress}{Strain}}</math>

<math> Stress = {\frac{F_{tension}}{Area_{Cross Sectional}}} </math>

<math> Strain = {\frac{ΔL_{wire}}{L_{0}}} </math>

===Speeds of Various Compositions===
[[File:speedofsound.jpg]]

==Examples==

Be sure to show all steps in your solution and include diagrams whenever possible

===Theoretical===

Two metal rods are made of different elements. The interatomic spring stiffness of element A is four times larger than the interatomic spring stiffness for element B. The mass of an atom of element A is four times greater than the mass of an atom of element B. The atomic diameters are approximately the same for A and B. What is the ratio of the speed of sound in rod A to the speed of sound in rod B?

Solution: In this situation, the ratio of the speed of sound in rod A to the speed of sound in rod B is 1.

Looking at the formula for computing speed of sound in solids, <math> {V_{s}} = d* √ (K_{s}/m_{atom}) </math>, you see that velocity depends three factors, interatomic stiffness, the mass of one atom, and interatomic bond length. The two rods differences in atomic mass and interatomic stiffness offset each other when the equations are set equal, and the ratio is determined to be 1.

<math> d* √ 4(K_{s}/m_{atom}) = d* √ (K_{s}/4m_{atom}) </math> After simplification <math> V_{s_{1}} = V_{s{2}} </math>

===Numerical Example ===
The Young's Modulus value of silver is 7.75e+10, atomic mass of silver is 108 g/mole, and the density of silver is 10.5 g/cm3. Using this information, calculate the speed of sound in silver.

Solution: The key to solving this problem is to realize the micro-macro connection of Young's Modulus. You are given that Young's Modulus is equal to 7.75e+10, and we know that
Youngs Modulus = (<math> K_{s}/d </math>). In this situation, we need to calculate the interatomic bond length and use it and our Young's Modulus value to determine our interatomic stiffness.

To solve for ''d'', we use the given density of silver (10.5 g/cm3). Using the basic equation for volume in relation to density and mass (<math> V=m*d</math>), we can find ''d'', since ''d'' is equal to the cube root of volume.

Once ''d'' is solved for, it can be plugged back into the the equation <math> Y = K_{s}/d </math> to solve for <math> K_{s} </math>

Now, we have solved for both interatomic bond length and stiffness. The only quantity in the final speed of sound equation we need is the mass of one atom, which can be determined using Avogardro's number and the atomic mass. <math> m_{atom} = </math> ''atomic mass'' / <math> 6.022e23 </math>

Now that all variables are solved for, we can substitute values into our <math> {V_{s}} = d* √ (K_{s}/m_{atom}) </math> equation.

<math> {V_{s}} = 1.6e-10* √ (78534.7/1.79e-22) </math>

<math> {V_{s}} = 2723</math> m/s

==Connectedness==
The computation of speed of sound in solids is dependent on a mass' interatomic properties, such as interatomic bond length. I find it interesting when a object's interatomic properties determine its functionality on a larger scale. In the case of speed of sound in solids, the objects elasticity depends on the interatomic bond length.

While the computation of speed of sound in solids may not seem related to Industrial Engineering, it has clear implications in the process of choosing building materials, which is a notable section of industrial engineering. For example, if you are planning to build something soundproof, it would be optimal to choose a solid with a very low speed of sound velocity.

The industrial applications in terms of construction are vast. An objects ability to block/allow sound waves through it is very important. Of course, insulation materials and sound proof wall materials come to thought at first. However, in some cases, contractors need to build structures that allow sound to travel through, in which they would choose solid materials that correlate with high speeds of sound.

==History==

The speed of sound in air was first measured by Sir Isaac Newton, and first correctly computed by Pierre-Simon Laplace in 1816. Before this precise measurement, attempts had been made across Europe during the 1700s, most famously Reverend William Derham's experiment in 1709 across the town of Upminister, England. Reverend Derham used a shotgun's noise and several known landmarks around time to measure the time it took for the sound of the blast to be heard from select distances.

Young's Modulus was named after English physicist Thomas Young. In actuality, the concept was developed earlier by physicists Leonhard Euler and Giordano Riccati in the 1720s.

== See also ==

Youngs Modulus: [http://www.physicsbook.gatech.edu/Young%27s_Modulus]
Interatomic Bonds: [http://www.physicsbook.gatech.edu/Length_and_Stiffness_of_an_Interatomic_Bond]

===Further reading===

Further Information can be found on the speed of sound in solids in ''Matter and Interactions, 4th Edition'' by Ruth W. Chabay & Bruce A. Sherwood
===External links===

Internet resources on this topic can be found at:

Engineering Tool Box [http://www.engineeringtoolbox.com/sound-speed-solids-d_713.html]

Hyperphysics [http://hyperphysics.phy-astr.gsu.edu/hbase/sound/souspe2.html]

Potto Project [http://www.potto.org/gasDynamics/node73.html]

NDT Resource Center [https://www.nde-ed.org/EducationResources/CommunityCollege/Ultrasonics/Physics/elasticsolids.htm]

==References==

This section contains the the references used while writing this page

Chart from [http://www.rcgroups.com/forums/attachment.php?attachmentid=3397792]

''Matter and Interactions 4th Edition'' by Chabay and Sherwood

Wikipage created by Daiven Patel

Hardness

2016-11-08T22:25:50Z

Achawki3:

CLAIMED BY ANTHONY CHAWKI
Hardness is the measure of how well a solid object can resist shape change when being exposed to compressive forces.

==The Main Idea==

===Properties of Matter===
Properties of matter are divided into two categories, chemical and physical. Hardness falls in the physical category; it can be determined without altering the matter. It is an unusual property because it is not an intrinsic property which can be defined in terms of fundamental SI units. Hardness can be difficult to calculate.

===Hardness===
Hardness is the measure of how well a solid object can resist shape change when being exposed to compressive forces. There is a link between hardness and chemical composition. This is due to the solid matter's crystal structure.

===Why it matters===
Solid matter generally has 3 responses to forces, depending on the force type and amount. Elasticity, plasticity, and fracture. Elasticity is the ability to return to original shape after force has been applied. Plasticity is the solid matter's ability to remain one piece. Fracture is when the solid matter splits into two or more pieces. Stress versus strain graphs show how these responses are related. Hardness matters because it is important to know what matters will be able to withstand certain forces and be resistant to deformation, indentation, or penetration.

[[File:Stressvsstrain.png]]
==Calculating Hardness==

There is no one way of calculating hardness. In fact, there are many hardness tests, such as Brinell, Knoop, Rockwell, and Vickers.

===Sensitivity Coefficient===
These tests can be improved by the introduction of a sensitivity coefficient. Sensitivity coefficients are used to determine the factor that different parameters, such as force, diameter, and depth have on hardness.

The Sensitivity coefficient ci, is defined as the change in hardness H, over the input parameter xi:

ci = ΔH/Δxi

==Examples and History==

===Mohs hardness scale===
There is no standard hardness scale, but of the Mohs scale is the most commonly used. The Mohs scale of mineral hardness organizes the scratch resistance of various minerals. It does this by determining and ranking the ability of a harder material to scratch a softer material. It is named after its creator, Friedrich Mohs, a German mineralogist.

== See also ==
https://en.wikipedia.org/wiki/Mohs_scale_of_mineral_hardness

http://www.npl.co.uk/upload/pdf/brinell_hardness_co.pdf

http://www.npl.co.uk/upload/pdf/vickers_hardness_co.pdf

===External links===

http://physicsworld.com/cws/article/news/2006/mar/09/how-to-calculate-hardness

==References==

http://physicsworld.com/cws/article/news/2006/mar/09/how-to-calculate-hardness

http://chemwiki.ucdavis.edu/Analytical_Chemistry/Chemical_Reactions/Properties_of_Matter

https://en.wikipedia.org/wiki/Mohs_scale_of_mineral_hardness

https://en.wikipedia.org/wiki/File:Stress-strain1.svg

http://www.npl.co.uk/science-technology/mass-and-force/hardness/

[[Category:Properties of Matter]]

Sarah Gould