Physics Book - User contributions [en]

Scattering: Collisions in 2D and 3D

2017-04-10T01:14:37Z

Ezhao7: /* Examples */

Edwin Zhao - Spring 17

==The Main Idea==

Scattering (Rutherford Scattering) is a type of experiment that is used to study the structure and behavior of atoms, nuclei, and other small particles. This allows us to understand small particles on a greater level.

Unlike normal collisions, atomic and nuclear collisions are far too small to observe the curving trajectories of the interacting particles. The only thing
that can be noticed is the initial and final states of the interaction. Therefore, the method pertained of alpha particles from a radioactive source striking a thin gold foil. Since it is only noticed a very small number of atoms are scattered after contact with the gold, it can be determined that the majority of the material is positively charged and when the alpha particle (positive) travels through and approaches close enough to the nucleus, it will repel and then "scatter" into a large angle.

By finding the back-scattering, it shows that atoms are arranged tightly together. Scattering experiments are incorporated in the world of collisions
to be able to study the minute details (structure) of atoms, nuclei, and other tiny particles as the interact with one another.

After collision with the gold nucleus, the alpha particle gets deflected some angle θ. The gold nucleus recoils at some angle Φ. It is important to pick optimal time frames ("before" early enough and "after" late enough) so that the two particles are far away enough from each other to avoid their electric potential energies. The speeds in this approach are small in comparison to the speed of light.

The case of which Rutherford scattering of alpha particles with gold nuclei is an example of elastic scattering because the initial and final velocity and energy stay the exact same.

==Equations==

<math>{p_xi = p_xf}</math>

<math>{p_1 = p_3 cosθ + p_4 cosΦ}</math>

<math>{p_yi = p_yf}</math>

<math>{0 = p_3 cos(90° - θ) + p_4 cos(90° + Φ)}</math>

<math>{K_f = K_i}</math>

<math>{\frac{p^2_1}{2m} = \frac{p^2_3}{2m} + \frac{p^2_4}{2M}}</math>

Where <math>{p_1, p_3, and p_4}</math> are all magnitudes of the momenta. It can be remembered that the gold nucleus is initially at rest.

The directions of cosine are used to express vector components to the x-axis.

ex. Final momentum of gold nucleus <math>{= \vec{p_4} = |\vec{p_4}| < cosΦ, cos(90° + Φ), 0>}</math>

==Impact Parameters==
Definition: The distance between centers perpendicular to the incoming velocity. Impact parameter is often denoted by the variable b.

A head-on collision has an impact parameter of zero and with equal masses fully transfers the momentum such as with Newton's Cradle. As the impact parameter gets smaller the collision has a larger effect, and an even large deflection angle (scattering).

''Elastic collisions between two billiard balls''

[[File:impactParamEx.jpg]]

==Examples==
===Simple===
The collision of an alpha particle (helium nucleus) with the nucleus of a gold atom

===Scattering in 2D===

[[File:scatteringExample.png]]
[[https://phet.colorado.edu/sims/html/rutherford-scattering/latest/rutherford-scattering_en.html Rutherford Scattering Example]]

As alpha particles approach the Rutherford atom in the center, they are repelled from it. The closer the alpha particles are to the atom in the center, the more they are repelled. These closer alpha particles are repelled to sometimes angles of greater than 100°.

==History==

In 1871 Lord Rayleigh published a paper on scattering. Rayleigh scattering is the dispersion of electromagnetic radiation by particles that have a minute radius less than approximately 1/10 the wavelength. It laid the foundation to research on scattering and information we have today.

In Ernest Rutherford's laboratory with Hans Geiger and Ernest Marsden, they experimented with tests of scattering alpha particles with thin metal foils. In 1909, Geiger and Marsden discovered scattering through their [https://en.wikipedia.org/wiki/Geiger%E2%80%93Marsden_experiment gold foil experiments.] From this, they discovered that some alpha particles scattered at angles greater than 90°.

== See also ==

[[Category:Collisions] (Main page)

===Further reading===

Matter and Interactions, Volume I: Modern Mechanics, 4th Edition. (Chapter 10.6)

===External links===
[http://physics-animations.com/Physics/English/par_txt.htm]
[http://www.britannica.com/science/Rayleigh-scattering]
[http://hypernews.slac.stanford.edu/slacsite/aux/HiPPP/scattering/]

==References==

Chabay, Ruth W., Bruce Sherwood. Matter and Interactions, Volume I: Modern Mechanics, 4th Edition. Wiley, 19/2014.

[[Category:Collisions]]

File:ScatteringExample.png

2017-04-10T01:11:20Z

Ezhao7:

Scattering: Collisions in 2D and 3D

2017-04-09T23:07:28Z

Ezhao7: /* The Main Idea */

Edwin Zhao - Spring 17

==The Main Idea==

Scattering (Rutherford Scattering) is a type of experiment that is used to study the structure and behavior of atoms, nuclei, and other small particles. This allows us to understand small particles on a greater level.

Unlike normal collisions, atomic and nuclear collisions are far too small to observe the curving trajectories of the interacting particles. The only thing
that can be noticed is the initial and final states of the interaction. Therefore, the method pertained of alpha particles from a radioactive source striking a thin gold foil. Since it is only noticed a very small number of atoms are scattered after contact with the gold, it can be determined that the majority of the material is positively charged and when the alpha particle (positive) travels through and approaches close enough to the nucleus, it will repel and then "scatter" into a large angle.

By finding the back-scattering, it shows that atoms are arranged tightly together. Scattering experiments are incorporated in the world of collisions
to be able to study the minute details (structure) of atoms, nuclei, and other tiny particles as the interact with one another.

After collision with the gold nucleus, the alpha particle gets deflected some angle θ. The gold nucleus recoils at some angle Φ. It is important to pick optimal time frames ("before" early enough and "after" late enough) so that the two particles are far away enough from each other to avoid their electric potential energies. The speeds in this approach are small in comparison to the speed of light.

The case of which Rutherford scattering of alpha particles with gold nuclei is an example of elastic scattering because the initial and final velocity and energy stay the exact same.

==Equations==

<math>{p_xi = p_xf}</math>

<math>{p_1 = p_3 cosθ + p_4 cosΦ}</math>

<math>{p_yi = p_yf}</math>

<math>{0 = p_3 cos(90° - θ) + p_4 cos(90° + Φ)}</math>

<math>{K_f = K_i}</math>

<math>{\frac{p^2_1}{2m} = \frac{p^2_3}{2m} + \frac{p^2_4}{2M}}</math>

Where <math>{p_1, p_3, and p_4}</math> are all magnitudes of the momenta. It can be remembered that the gold nucleus is initially at rest.

The directions of cosine are used to express vector components to the x-axis.

ex. Final momentum of gold nucleus <math>{= \vec{p_4} = |\vec{p_4}| < cosΦ, cos(90° + Φ), 0>}</math>

==Impact Parameters==
Definition: The distance between centers perpendicular to the incoming velocity. Impact parameter is often denoted by the variable b.

A head-on collision has an impact parameter of zero and with equal masses fully transfers the momentum such as with Newton's Cradle. As the impact parameter gets smaller the collision has a larger effect, and an even large deflection angle (scattering).

''Elastic collisions between two billiard balls''

[[File:impactParamEx.jpg]]

==Examples==
===Simple===
The collision of an alpha particle (helium nucleus) with the nucleus of a gold atom

==History==

In 1871 Lord Rayleigh published a paper on scattering. Rayleigh scattering is the dispersion of electromagnetic radiation by particles that have a minute radius less than approximately 1/10 the wavelength. It laid the foundation to research on scattering and information we have today.

In Ernest Rutherford's laboratory with Hans Geiger and Ernest Marsden, they experimented with tests of scattering alpha particles with thin metal foils. In 1909, Geiger and Marsden discovered scattering through their [https://en.wikipedia.org/wiki/Geiger%E2%80%93Marsden_experiment gold foil experiments.] From this, they discovered that some alpha particles scattered at angles greater than 90°.

== See also ==

[[Category:Collisions] (Main page)

===Further reading===

Matter and Interactions, Volume I: Modern Mechanics, 4th Edition. (Chapter 10.6)

===External links===
[http://physics-animations.com/Physics/English/par_txt.htm]
[http://www.britannica.com/science/Rayleigh-scattering]
[http://hypernews.slac.stanford.edu/slacsite/aux/HiPPP/scattering/]

==References==

Chabay, Ruth W., Bruce Sherwood. Matter and Interactions, Volume I: Modern Mechanics, 4th Edition. Wiley, 19/2014.

[[Category:Collisions]]

Scattering: Collisions in 2D and 3D

2017-04-09T22:50:48Z

Ezhao7:

Edwin Zhao - Spring 17

==The Main Idea==

Scattering (Rutherford Scattering) is a type of experiment that is used to study the structure and behavior of atoms, nuclei, and other small particles. This allows us to understand small particles on a greater level.

Unlike normal collisions, atomic and nuclear collisions are far too small to observe the curving trajectories of the interacting particles. The only thing
that can be noticed is the initial and final states of the interaction. Therefore, the method pertained of alpha particles from a radioactive source striking a thin gold foil.

By finding the back-scattering, it shows that atoms are arranged tightly together. Scattering experiments are incorporated in the world of collisions
to be able to study the minute details (structure) of atoms, nuclei, and other tiny particles as the interact with one another.

After collision with the gold nucleus, the alpha particle gets deflected some angle θ. The gold nucleus recoils at some angle Φ. It is important to pick optimal time frames ("before" early enough and "after" late enough) so that the two particles are far away enough from each other to avoid their electric potential energies. The speeds in this approach are small in comparison to the speed of light.

==Equations==

<math>{p_xi = p_xf}</math>

<math>{p_1 = p_3 cosθ + p_4 cosΦ}</math>

<math>{p_yi = p_yf}</math>

<math>{0 = p_3 cos(90° - θ) + p_4 cos(90° + Φ)}</math>

<math>{K_f = K_i}</math>

<math>{\frac{p^2_1}{2m} = \frac{p^2_3}{2m} + \frac{p^2_4}{2M}}</math>

Where <math>{p_1, p_3, and p_4}</math> are all magnitudes of the momenta. It can be remembered that the gold nucleus is initially at rest.

The directions of cosine are used to express vector components to the x-axis.

ex. Final momentum of gold nucleus <math>{= \vec{p_4} = |\vec{p_4}| < cosΦ, cos(90° + Φ), 0>}</math>

==Impact Parameters==
Definition: The distance between centers perpendicular to the incoming velocity. Impact parameter is often denoted by the variable b.

A head-on collision has an impact parameter of zero and with equal masses fully transfers the momentum such as with Newton's Cradle. As the impact parameter gets smaller the collision has a larger effect, and an even large deflection angle (scattering).

''Elastic collisions between two billiard balls''

[[File:impactParamEx.jpg]]

==Examples==
===Simple===
The collision of an alpha particle (helium nucleus) with the nucleus of a gold atom

==History==

In 1871 Lord Rayleigh published a paper on scattering. Rayleigh scattering is the dispersion of electromagnetic radiation by particles that have a minute radius less than approximately 1/10 the wavelength. It laid the foundation to research on scattering and information we have today.

In Ernest Rutherford's laboratory with Hans Geiger and Ernest Marsden, they experimented with tests of scattering alpha particles with thin metal foils. In 1909, Geiger and Marsden discovered scattering through their [https://en.wikipedia.org/wiki/Geiger%E2%80%93Marsden_experiment gold foil experiments.] From this, they discovered that some alpha particles scattered at angles greater than 90°.

== See also ==

[[Category:Collisions] (Main page)

===Further reading===

Matter and Interactions, Volume I: Modern Mechanics, 4th Edition. (Chapter 10.6)

===External links===
[http://physics-animations.com/Physics/English/par_txt.htm]
[http://www.britannica.com/science/Rayleigh-scattering]
[http://hypernews.slac.stanford.edu/slacsite/aux/HiPPP/scattering/]

==References==

Chabay, Ruth W., Bruce Sherwood. Matter and Interactions, Volume I: Modern Mechanics, 4th Edition. Wiley, 19/2014.

[[Category:Collisions]]

Scattering: Collisions in 2D and 3D

2017-04-09T22:33:58Z

Ezhao7: /* The Main Idea */

Scattering: Collisions in 2D and 3D

2017-04-09T22:28:00Z

Ezhao7: /* The Main Idea */

Scattering: Collisions in 2D and 3D

2017-04-09T20:13:41Z

Ezhao7: /* Impact Parameters */

Edwin Zhao - Spring 17

==The Main Idea==

Scattering (Rutherford Scattering) is a type of experiment that is used to study the structure and behavior of atoms, nuclei, and other small particles.

Unlike normal collisions, atomic and nuclear collisions are far too small to observe the curving trajectories of the interacting particles. The only thing
that can be noticed is the initial and final states of the interaction. Therefore, the method pertained of alpha particles from a radioactive source striking a thin gold foil.

By finding the back-scattering, it shows that atoms are arranged tightly together. Scattering experiments are incorporated in the world of collisions
to be able to study the minute details (structure) of atoms, nuclei, and other tiny particles as the interact with one another.

==Impact Parameters==
Definition: The distance between centers perpendicular to the incoming velocity. Impact parameter is often denoted by the variable b.

A head-on collision has an impact parameter of zero and with equal masses fully transfers the momentum such as with Newton's Cradle. As the impact parameter gets smaller the collision has a larger effect, and an even large deflection angle (scattering).

''Elastic collisions between two billiard balls''

[[File:impactParamEx.jpg]]

==Examples==
===Simple===
The collision of an alpha particle (helium nucleus) with the nucleus of a gold atom

==History==

In 1871 Lord Rayleigh published a paper on scattering. Rayleigh scattering is the dispersion of electromagnetic radiation by particles that have a minute radius less than approximately 1/10 the wavelength. It laid the foundation to research on scattering and information we have today.

In Ernest Rutherford's laboratory with Hans Geiger and Ernest Marsden, they experimented with tests of scattering alpha particles with thin metal foils. In 1909, Geiger and Marsden discovered scattering through their [https://en.wikipedia.org/wiki/Geiger%E2%80%93Marsden_experiment gold foil experiments.] From this, they discovered that some alpha particles scattered at angles greater than 90°.

== See also ==

[[Category:Collisions] (Main page)

===Further reading===

Matter and Interactions, Volume I: Modern Mechanics, 4th Edition. (Chapter 10.6)

===External links===
[http://physics-animations.com/Physics/English/par_txt.htm]
[http://www.britannica.com/science/Rayleigh-scattering]
[http://hypernews.slac.stanford.edu/slacsite/aux/HiPPP/scattering/]

==References==

Chabay, Ruth W., Bruce Sherwood. Matter and Interactions, Volume I: Modern Mechanics, 4th Edition. Wiley, 19/2014.

[[Category:Collisions]]

File:ImpactParamEx.jpg

2017-04-09T20:13:11Z

Ezhao7:

Scattering: Collisions in 2D and 3D

2017-04-09T20:09:48Z

Ezhao7: /* Impact Parameters */

Edwin Zhao - Spring 17

==The Main Idea==

Scattering (Rutherford Scattering) is a type of experiment that is used to study the structure and behavior of atoms, nuclei, and other small particles.

Unlike normal collisions, atomic and nuclear collisions are far too small to observe the curving trajectories of the interacting particles. The only thing
that can be noticed is the initial and final states of the interaction. Therefore, the method pertained of alpha particles from a radioactive source striking a thin gold foil.

By finding the back-scattering, it shows that atoms are arranged tightly together. Scattering experiments are incorporated in the world of collisions
to be able to study the minute details (structure) of atoms, nuclei, and other tiny particles as the interact with one another.

==Impact Parameters==
Definition: The distance between centers perpendicular to the incoming velocity. Impact parameter is often denoted by the variable b.

A head-on collision has an impact parameter of zero and with equal masses fully transfers the momentum such as with Newton's Cradle. As the impact parameter gets smaller the collision has a larger effect, and an even large deflection angle (scattering).

Elastic collisions between two billiard balls
[[File:ImpactParameter.png]]

==Examples==
===Simple===
The collision of an alpha particle (helium nucleus) with the nucleus of a gold atom

==History==

In 1871 Lord Rayleigh published a paper on scattering. Rayleigh scattering is the dispersion of electromagnetic radiation by particles that have a minute radius less than approximately 1/10 the wavelength. It laid the foundation to research on scattering and information we have today.

In Ernest Rutherford's laboratory with Hans Geiger and Ernest Marsden, they experimented with tests of scattering alpha particles with thin metal foils. In 1909, Geiger and Marsden discovered scattering through their [https://en.wikipedia.org/wiki/Geiger%E2%80%93Marsden_experiment gold foil experiments.] From this, they discovered that some alpha particles scattered at angles greater than 90°.

== See also ==

[[Category:Collisions] (Main page)

===Further reading===

Matter and Interactions, Volume I: Modern Mechanics, 4th Edition. (Chapter 10.6)

===External links===
[http://physics-animations.com/Physics/English/par_txt.htm]
[http://www.britannica.com/science/Rayleigh-scattering]
[http://hypernews.slac.stanford.edu/slacsite/aux/HiPPP/scattering/]

==References==

Chabay, Ruth W., Bruce Sherwood. Matter and Interactions, Volume I: Modern Mechanics, 4th Edition. Wiley, 19/2014.

[[Category:Collisions]]

Scattering: Collisions in 2D and 3D

2017-04-09T20:09:33Z

Ezhao7: /* The Main Idea */

Edwin Zhao - Spring 17

==The Main Idea==

Scattering (Rutherford Scattering) is a type of experiment that is used to study the structure and behavior of atoms, nuclei, and other small particles.

Unlike normal collisions, atomic and nuclear collisions are far too small to observe the curving trajectories of the interacting particles. The only thing
that can be noticed is the initial and final states of the interaction. Therefore, the method pertained of alpha particles from a radioactive source striking a thin gold foil.

By finding the back-scattering, it shows that atoms are arranged tightly together. Scattering experiments are incorporated in the world of collisions
to be able to study the minute details (structure) of atoms, nuclei, and other tiny particles as the interact with one another.

==Impact Parameters==
Definition: The distance between centers perpendicular to the incoming velocity. Impact parameter is often denoted by the variable b.

A head-on collision has an impact parameter of zero and with equal masses fully transfers the momentum such as with Newton's Cradle. As the impact parameter gets smaller the collision has a larger effect, and an even large deflection angle (scattering).

Elastic collisions between two billiard balls (Double Click Image)
[[File:ImpactParameter.png]]

==Examples==
===Simple===
The collision of an alpha particle (helium nucleus) with the nucleus of a gold atom

==History==

In 1871 Lord Rayleigh published a paper on scattering. Rayleigh scattering is the dispersion of electromagnetic radiation by particles that have a minute radius less than approximately 1/10 the wavelength. It laid the foundation to research on scattering and information we have today.

In Ernest Rutherford's laboratory with Hans Geiger and Ernest Marsden, they experimented with tests of scattering alpha particles with thin metal foils. In 1909, Geiger and Marsden discovered scattering through their [https://en.wikipedia.org/wiki/Geiger%E2%80%93Marsden_experiment gold foil experiments.] From this, they discovered that some alpha particles scattered at angles greater than 90°.

== See also ==

[[Category:Collisions] (Main page)

===Further reading===

Matter and Interactions, Volume I: Modern Mechanics, 4th Edition. (Chapter 10.6)

===External links===
[http://physics-animations.com/Physics/English/par_txt.htm]
[http://www.britannica.com/science/Rayleigh-scattering]
[http://hypernews.slac.stanford.edu/slacsite/aux/HiPPP/scattering/]

==References==

Chabay, Ruth W., Bruce Sherwood. Matter and Interactions, Volume I: Modern Mechanics, 4th Edition. Wiley, 19/2014.

[[Category:Collisions]]

Scattering: Collisions in 2D and 3D

2017-04-09T20:07:48Z

Ezhao7: /* The Main Idea */

Edwin Zhao - Spring 17

==The Main Idea==

Scattering (Rutherford Scattering) is a type of experiment that is used to study the structure and behaviour of atoms, nuclei, and other small particles.

Unlike normal collisions, atomic and nuclear collisions are far too small to observe the curving trajectories of the interacting particles. The only thing that can be noticed is the initial and final states of the interaction. Therefore, the method pertained of alpha particles from a radioactive source striking a thin gold foil.

By finding the back-scattering, it shows that atoms are arranged tightly together.. Scattering experiments are incorporated in the world of collisions to be able to study the minute details (structure) of atoms, nuclei, and other tiny particles as the interact with one another.

==Impact Parameters==
Definition: The distance between centers perpendicular to the incoming velocity. Impact parameter is often denoted by the variable b.

A head-on collision has an impact parameter of zero and with equal masses fully transfers the momentum such as with Newton's Cradle. As the impact parameter gets smaller the collision has a larger effect, and an even large deflection angle (scattering).

Elastic collisions between two billiard balls (Double Click Image)
[[File:ImpactParameter.png]]

==Examples==
===Simple===
The collision of an alpha particle (helium nucleus) with the nucleus of a gold atom

==History==

In 1871 Lord Rayleigh published a paper on scattering. Rayleigh scattering is the dispersion of electromagnetic radiation by particles that have a minute radius less than approximately 1/10 the wavelength. It laid the foundation to research on scattering and information we have today.

In Ernest Rutherford's laboratory with Hans Geiger and Ernest Marsden, they experimented with tests of scattering alpha particles with thin metal foils. In 1909, Geiger and Marsden discovered scattering through their [https://en.wikipedia.org/wiki/Geiger%E2%80%93Marsden_experiment gold foil experiments.] From this, they discovered that some alpha particles scattered at angles greater than 90°.

== See also ==

[[Category:Collisions] (Main page)

===Further reading===

Matter and Interactions, Volume I: Modern Mechanics, 4th Edition. (Chapter 10.6)

===External links===
[http://physics-animations.com/Physics/English/par_txt.htm]
[http://www.britannica.com/science/Rayleigh-scattering]
[http://hypernews.slac.stanford.edu/slacsite/aux/HiPPP/scattering/]

==References==

Chabay, Ruth W., Bruce Sherwood. Matter and Interactions, Volume I: Modern Mechanics, 4th Edition. Wiley, 19/2014.

[[Category:Collisions]]

Scattering: Collisions in 2D and 3D

2017-04-09T20:07:30Z

Ezhao7: /* The Main Idea */

Edwin Zhao - Spring 17

==The Main Idea==

Scattering (Rutherford Scattering) is a type of experiment that is used to study the structure and behaviour of atoms, nuclei, and other small particles.
Unlike normal collisions, atomic and nuclear collisions are far too small to observe the curving trajectories of the interacting particles. The only thing that can be noticed is the initial and final states of the interaction. Therefore, the method pertained of alpha particles from a radioactive source striking a thin gold foil. By finding the back-scattering, it shows that atoms are arranged tightly together.. Scattering experiments are incorporated in the world of collisions to be able to study the minute details (structure) of atoms, nuclei, and other tiny particles as the interact with one another.

==Impact Parameters==
Definition: The distance between centers perpendicular to the incoming velocity. Impact parameter is often denoted by the variable b.

A head-on collision has an impact parameter of zero and with equal masses fully transfers the momentum such as with Newton's Cradle. As the impact parameter gets smaller the collision has a larger effect, and an even large deflection angle (scattering).

Elastic collisions between two billiard balls (Double Click Image)
[[File:ImpactParameter.png]]

==Examples==
===Simple===
The collision of an alpha particle (helium nucleus) with the nucleus of a gold atom

==History==

In 1871 Lord Rayleigh published a paper on scattering. Rayleigh scattering is the dispersion of electromagnetic radiation by particles that have a minute radius less than approximately 1/10 the wavelength. It laid the foundation to research on scattering and information we have today.

In Ernest Rutherford's laboratory with Hans Geiger and Ernest Marsden, they experimented with tests of scattering alpha particles with thin metal foils. In 1909, Geiger and Marsden discovered scattering through their [https://en.wikipedia.org/wiki/Geiger%E2%80%93Marsden_experiment gold foil experiments.] From this, they discovered that some alpha particles scattered at angles greater than 90°.

== See also ==

[[Category:Collisions] (Main page)

===Further reading===

Matter and Interactions, Volume I: Modern Mechanics, 4th Edition. (Chapter 10.6)

===External links===
[http://physics-animations.com/Physics/English/par_txt.htm]
[http://www.britannica.com/science/Rayleigh-scattering]
[http://hypernews.slac.stanford.edu/slacsite/aux/HiPPP/scattering/]

==References==

Chabay, Ruth W., Bruce Sherwood. Matter and Interactions, Volume I: Modern Mechanics, 4th Edition. Wiley, 19/2014.

[[Category:Collisions]]

Scattering: Collisions in 2D and 3D

2017-04-07T01:23:35Z

Ezhao7: /* History */

Edwin Zhao - Spring 17

==The Main Idea==

Scattering (Rutherford Scattering) is a type of experiment that is used to study the structure and behaviour of atoms, nuclei, and other small particles.
Unlike normal collisions, atomic and nuclear collisions are far too small to observe the curving trajectories of the interacting particles. The only thing that can be noticed is the initial and final states of the interaction. Scattering experiments are incorporated in the world of collisions to be able to study the minute details (structure) of atoms, nuclei, and other tiny particles as the interact with one another.

==Impact Parameters==
Definition: The distance between centers perpendicular to the incoming velocity. Impact parameter is often denoted by the variable b.

A head-on collision has an impact parameter of zero and with equal masses fully transfers the momentum such as with Newton's Cradle. As the impact parameter gets smaller the collision has a larger effect, and an even large deflection angle (scattering).

Elastic collisions between two billiard balls (Double Click Image)
[[File:ImpactParameter.png]]

==Examples==
===Simple===
The collision of an alpha particle (helium nucleus) with the nucleus of a gold atom

==History==

In 1871 Lord Rayleigh published a paper on scattering. Rayleigh scattering is the dispersion of electromagnetic radiation by particles that have a minute radius less than approximately 1/10 the wavelength. It laid the foundation to research on scattering and information we have today.

In Ernest Rutherford's laboratory with Hans Geiger and Ernest Marsden, they experimented with tests of scattering alpha particles with thin metal foils. In 1909, Geiger and Marsden discovered scattering through their [https://en.wikipedia.org/wiki/Geiger%E2%80%93Marsden_experiment gold foil experiments.] From this, they discovered that some alpha particles scattered at angles greater than 90°.

== See also ==

[[Category:Collisions] (Main page)

===Further reading===

Matter and Interactions, Volume I: Modern Mechanics, 4th Edition. (Chapter 10.6)

===External links===
[http://physics-animations.com/Physics/English/par_txt.htm]
[http://www.britannica.com/science/Rayleigh-scattering]
[http://hypernews.slac.stanford.edu/slacsite/aux/HiPPP/scattering/]

==References==

Chabay, Ruth W., Bruce Sherwood. Matter and Interactions, Volume I: Modern Mechanics, 4th Edition. Wiley, 19/2014.

[[Category:Collisions]]

Scattering: Collisions in 2D and 3D

2017-04-07T00:46:06Z

Ezhao7: /* The Main Idea */

Edwin Zhao - Spring 17

==The Main Idea==

Scattering (Rutherford Scattering) is a type of experiment that is used to study the structure and behaviour of atoms, nuclei, and other small particles.
Unlike normal collisions, atomic and nuclear collisions are far too small to observe the curving trajectories of the interacting particles. The only thing that can be noticed is the initial and final states of the interaction. Scattering experiments are incorporated in the world of collisions to be able to study the minute details (structure) of atoms, nuclei, and other tiny particles as the interact with one another.

==Impact Parameters==
Definition: The distance between centers perpendicular to the incoming velocity. Impact parameter is often denoted by the variable b.

A head-on collision has an impact parameter of zero and with equal masses fully transfers the momentum such as with Newton's Cradle. As the impact parameter gets smaller the collision has a larger effect, and an even large deflection angle (scattering).

Elastic collisions between two billiard balls (Double Click Image)
[[File:ImpactParameter.png]]

==Examples==
===Simple===
The collision of an alpha particle (helium nucleus) with the nucleus of a gold atom

==History==

In 1871 Lord Rayleigh published a paper on scattering. Rayleigh scattering is the dispersion of electromagnetic radiation by particles that have a minute radius less than approximately 1/10 the wavelength. It laid the foundation to research on scattering and information we have today.

== See also ==

[[Category:Collisions] (Main page)

===Further reading===

Matter and Interactions, Volume I: Modern Mechanics, 4th Edition. (Chapter 10.6)

===External links===
[http://physics-animations.com/Physics/English/par_txt.htm]
[http://www.britannica.com/science/Rayleigh-scattering]
[http://hypernews.slac.stanford.edu/slacsite/aux/HiPPP/scattering/]

==References==

Chabay, Ruth W., Bruce Sherwood. Matter and Interactions, Volume I: Modern Mechanics, 4th Edition. Wiley, 19/2014.

[[Category:Collisions]]

Second Law of Thermodynamics and Entropy

2017-04-02T20:08:14Z

Ezhao7:

Alyssa Candelmo (acandelmo6)

==The Main Idea==

Entropy represents the quantity of the unavailability of a systems thermal energy to be converted into mechanical work. The entropy of the system can also be described as the systems level of disorder or randomness. The more entropy a system has, the more random it will be. The second law of thermodynamics states that the entropy of the universe will always increase over time. The second law also states that change in the entropy of the universe will never be negative. Essentially, through the discovery that heat can not spontaneously flow from a colder body to a hotter body, physicists also discovered that is impossible to complete any physical process without the loss of some useable energy. As time goes on, randomness can only increase.

[[File:Entropy.gif|center|border]]

==A Mathematical Model==

''Boltzmann's Equation: '''''ΔS'' = K ''lnΩ''''' ''

: Where ΔS is the change in entropy of the system

: ''K'' is the Boltzmann's Constant (or 1.38065 × 10‾²³ J/K)

: Ω is the number of microstates corresponding to a given macro state

''The Second Law of Thermodynamics: '''ΔS = ΔQ/T'', and ∫ΔQ/T ≤ 0'''

: Where ''ΔS'' is the change in entropy of the system

: ''ΔQ'' is the change in heat of the system,

: ''T'' is the temperature at the point where the heat transfer took place

==Example==

Considering the cycle made by taking path A followed by path B, using the given calculated integrals, determine if the cycle is reversible, irreversible, or impossible.

[[File:Cycle.png|right|border]]

[[File:I1.png|right|border]]

[[File:I2.png|right|border]]

We use the second law of thermodynamics and the Clausius inequality(∫ΔQ/T ≤ 0) to draw the conclusions that if the cyclic integral is:

*''Positive:'' the cycle is impossible

*''Negative:'' the cycle is irreversible

*''Zero:'' the cycle is reversible

[[File:I3.png]]

We use the equation above to include both paths in our cycle, and plug in their given values.

∫ΔQ/T = -27.7 + 41.3 = '''16.6'''

Because the value is > 0, we conclude that the cycle is impossible.

==Connectedness==

===How is this topic connected to something that you are interested in?===
For someone who loves to cook as much as I do, entropy plays a surprisingly large role. For example, entropy is the reason that Crystal Light power resolves in water. Over time, the particles spread and spread because the more spaced out they are, the more disorderly they are. And as we know, disorder must increase with time.

===How is it connected to your major?===

As an Industrial and Systems Engineering Major, a lot of the work I do will be designing production plants to be as efficient as they can possibly be. Understanding the concept of entropy and that no physical process can be completed without the loss of energy will help me to be able to account for that energy loss in my plans so that I can minimize the amount of inefficiency that occurs because of it. To understand that disorder is inherently more probable than order can help me be aware of more possible outcomes.

===Is there an interesting industrial application?===

The second law of thermodynamics is especially used in any industry making insulted products. Well, it is not "used" so much as it is fought against. Using the specifics of the second law of thermodynamics, companies who make thermos' or lunch boxes or insulation need to understand entropy and the second law to learn how to best fight heat dissipation so that they can keep hot things hot and cold thing cold.

==History==

===Contributors in the Development of the Second Law:===
[[File:Carnot.jpg|thumb|90px|Nicholas Carnot]]
*'''Nicholas Léonard Sadi Carnot''' (1 June 1796 – 24 August 1832)
**Considered to be the father of Thermodynamics
**Major Scientific Contributions:
***Carnot heat engine
***Carnot theorem
***Carnot efficiency
**His research was centered around learning if the work available from a heat source was limited, and whether the efficiency of a heat engine could be improved upon by replacing steam with a different substance
[[File:Clausius.jpg|thumb|90px|Rudolf Clausius]]
*'''Rudolf Clausius''' ( 2 January 1822 – 24 August 1888)
**German Physicist
**Developed the Clausius statement, which states that in general, heat can not flow spontaneously from a low temperature to a high temperature
**Wrote a famous paper titled "On the Moving Force of Heat and the Laws of Heat which May be Deduced Therefrom"
***Pointed out differences between the concept of conservation of energy
***Stated that assumptions about the Caloric theory were incorrect
**Presented the idea of Entropy and named it as such
**Was known for taking a mathematical approach to physics
[[File:Thompson.jpg|thumb|90px|William Thompson]]
*'''William Thompson''' (26 June 1824 – 17 December 1907)
**Also known as First Baron Kelvin
**Mathematical physicist and engineer
**Formulated the Kelvin Statement, which states that there is no way to convert all of the energy in a given system into work without losing energy
**Developed the vortex theory of the atom
**In addition to his contributions to thermodynamics, he also created the Kelvin scale
[[File:Caratheodory.jpg|thumb|90px|Constantin Caratheodory]]
*'''Constantin Carathéodory''' (13 September 1873 – 2 February 1950)
**German mathematician of Greek origin
**Principle of Caratheodory
**Took on thermodynamics with a mathematical axiomatic foundation
**Created his own version of the Second Law of Thermodynamics by stating that "In the neighborhood of any initial state, there are states which cannot be approached arbitrarily close through adiabatic changes of state."
**Used differential equations and Pfaffian expressions to prove the existence of entropy

== See also ==
[[The Energy Principle]]

[[Conservation of Energy]]

[[Thermal Energy]]

[[Energy Transfer due to a Temperature Difference]]

[[Work]]

==Further reading==

http://web.ist.utl.pt/berberan/data/68.pdf

https://www.youtube.com/watch?v=ByA_TBfMZe4

==References==

http://chemwiki.ucdavis.edu/Physical_Chemistry/Thermodynamics/Laws_of_Thermodynamics/Second_Law_of_Thermodynamics

https://www.asme.org/engineering-topics/articles/energy/nicolas-leonard-sadi-carnot

http://physics.stackexchange.com/questions/113847/principle-of-caratheodory-and-the-second-law-of-thermodynamics

http://digital.nls.uk/scientists/biographies/lord-kelvin/

http://www.eoht.info/page/Caratheodory’s+theorem

http://chemwiki.ucdavis.edu/Physical_Chemistry/Thermodynamics/State_Functions/Entropy

http://www.panspermia.org/seconlaw.htm

http://www.theguardian.com/science/2013/dec/01/what-is-the-second-law-of-thermodynamics

https://www.quora.com/Given-that-it-costs-energy-to-desalinate-water-is-there-any-way-to-release-energy-in-a-usable-form-by-resalinating-it

http://www.learnthermo.com/examples/example-problem.php?ch=7&lesson=A&problem=1

http://entropysimple.oxy.edu/content.htm

[[Category:Energy]]

Scattering: Collisions in 2D and 3D

2017-04-02T20:07:57Z

Ezhao7:

Edwin Zhao - Spring 17

==The Main Idea==

Unlike normal collisions, atomic and nuclear collisions are far too small to observe the curving trajectories of the interacting particles. The only thing that can be noticed is the initial and final states of the interaction. Scattering experiments are incorporated in the world of collisions to be able to study the minute details (structure) of atoms, nuclei, and other tiny particles as the interact with one another.

==Impact Parameters==
Definition: The distance between centers perpendicular to the incoming velocity. Impact parameter is often denoted by the variable b.

A head-on collision has an impact parameter of zero and with equal masses fully transfers the momentum such as with Newton's Cradle. As the impact parameter gets smaller the collision has a larger effect, and an even large deflection angle (scattering).

Elastic collisions between two billiard balls (Double Click Image)
[[File:ImpactParameter.png]]

==Examples==
===Simple===
The collision of an alpha particle (helium nucleus) with the nucleus of a gold atom

==History==

In 1871 Lord Rayleigh published a paper on scattering. Rayleigh scattering is the dispersion of electromagnetic radiation by particles that have a minute radius less than approximately 1/10 the wavelength. It laid the foundation to research on scattering and information we have today.

== See also ==

[[Category:Collisions] (Main page)

===Further reading===

Matter and Interactions, Volume I: Modern Mechanics, 4th Edition. (Chapter 10.6)

===External links===
[http://physics-animations.com/Physics/English/par_txt.htm]
[http://www.britannica.com/science/Rayleigh-scattering]
[http://hypernews.slac.stanford.edu/slacsite/aux/HiPPP/scattering/]

==References==

Chabay, Ruth W., Bruce Sherwood. Matter and Interactions, Volume I: Modern Mechanics, 4th Edition. Wiley, 19/2014.

[[Category:Collisions]]

Second Law of Thermodynamics and Entropy

2017-03-27T09:16:28Z

Ezhao7:

Alyssa Candelmo (acandelmo6)

Edwin Zhao (ezhao7) Spring 17

==The Main Idea==

Entropy represents the quantity of the unavailability of a systems thermal energy to be converted into mechanical work. The entropy of the system can also be described as the systems level of disorder or randomness. The more entropy a system has, the more random it will be. The second law of thermodynamics states that the entropy of the universe will always increase over time. The second law also states that change in the entropy of the universe will never be negative. Essentially, through the discovery that heat can not spontaneously flow from a colder body to a hotter body, physicists also discovered that is impossible to complete any physical process without the loss of some useable energy. As time goes on, randomness can only increase.

[[File:Entropy.gif|center|border]]

==A Mathematical Model==

''Boltzmann's Equation: '''''ΔS'' = K ''lnΩ''''' ''

: Where ΔS is the change in entropy of the system

: ''K'' is the Boltzmann's Constant (or 1.38065 × 10‾²³ J/K)

: Ω is the number of microstates corresponding to a given macro state

''The Second Law of Thermodynamics: '''ΔS = ΔQ/T'', and ∫ΔQ/T ≤ 0'''

: Where ''ΔS'' is the change in entropy of the system

: ''ΔQ'' is the change in heat of the system,

: ''T'' is the temperature at the point where the heat transfer took place

==Example==

Considering the cycle made by taking path A followed by path B, using the given calculated integrals, determine if the cycle is reversible, irreversible, or impossible.

[[File:Cycle.png|right|border]]

[[File:I1.png|right|border]]

[[File:I2.png|right|border]]

We use the second law of thermodynamics and the Clausius inequality(∫ΔQ/T ≤ 0) to draw the conclusions that if the cyclic integral is:

*''Positive:'' the cycle is impossible

*''Negative:'' the cycle is irreversible

*''Zero:'' the cycle is reversible

[[File:I3.png]]

We use the equation above to include both paths in our cycle, and plug in their given values.

∫ΔQ/T = -27.7 + 41.3 = '''16.6'''

Because the value is > 0, we conclude that the cycle is impossible.

==Connectedness==

===How is this topic connected to something that you are interested in?===
For someone who loves to cook as much as I do, entropy plays a surprisingly large role. For example, entropy is the reason that Crystal Light power resolves in water. Over time, the particles spread and spread because the more spaced out they are, the more disorderly they are. And as we know, disorder must increase with time.

===How is it connected to your major?===

As an Industrial and Systems Engineering Major, a lot of the work I do will be designing production plants to be as efficient as they can possibly be. Understanding the concept of entropy and that no physical process can be completed without the loss of energy will help me to be able to account for that energy loss in my plans so that I can minimize the amount of inefficiency that occurs because of it. To understand that disorder is inherently more probable than order can help me be aware of more possible outcomes.

===Is there an interesting industrial application?===

The second law of thermodynamics is especially used in any industry making insulted products. Well, it is not "used" so much as it is fought against. Using the specifics of the second law of thermodynamics, companies who make thermos' or lunch boxes or insulation need to understand entropy and the second law to learn how to best fight heat dissipation so that they can keep hot things hot and cold thing cold.

==History==

===Contributors in the Development of the Second Law:===
[[File:Carnot.jpg|thumb|90px|Nicholas Carnot]]
*'''Nicholas Léonard Sadi Carnot''' (1 June 1796 – 24 August 1832)
**Considered to be the father of Thermodynamics
**Major Scientific Contributions:
***Carnot heat engine
***Carnot theorem
***Carnot efficiency
**His research was centered around learning if the work available from a heat source was limited, and whether the efficiency of a heat engine could be improved upon by replacing steam with a different substance
[[File:Clausius.jpg|thumb|90px|Rudolf Clausius]]
*'''Rudolf Clausius''' ( 2 January 1822 – 24 August 1888)
**German Physicist
**Developed the Clausius statement, which states that in general, heat can not flow spontaneously from a low temperature to a high temperature
**Wrote a famous paper titled "On the Moving Force of Heat and the Laws of Heat which May be Deduced Therefrom"
***Pointed out differences between the concept of conservation of energy
***Stated that assumptions about the Caloric theory were incorrect
**Presented the idea of Entropy and named it as such
**Was known for taking a mathematical approach to physics
[[File:Thompson.jpg|thumb|90px|William Thompson]]
*'''William Thompson''' (26 June 1824 – 17 December 1907)
**Also known as First Baron Kelvin
**Mathematical physicist and engineer
**Formulated the Kelvin Statement, which states that there is no way to convert all of the energy in a given system into work without losing energy
**Developed the vortex theory of the atom
**In addition to his contributions to thermodynamics, he also created the Kelvin scale
[[File:Caratheodory.jpg|thumb|90px|Constantin Caratheodory]]
*'''Constantin Carathéodory''' (13 September 1873 – 2 February 1950)
**German mathematician of Greek origin
**Principle of Caratheodory
**Took on thermodynamics with a mathematical axiomatic foundation
**Created his own version of the Second Law of Thermodynamics by stating that "In the neighborhood of any initial state, there are states which cannot be approached arbitrarily close through adiabatic changes of state."
**Used differential equations and Pfaffian expressions to prove the existence of entropy

== See also ==
[[The Energy Principle]]

[[Conservation of Energy]]

[[Thermal Energy]]

[[Energy Transfer due to a Temperature Difference]]

[[Work]]

==Further reading==

http://web.ist.utl.pt/berberan/data/68.pdf

https://www.youtube.com/watch?v=ByA_TBfMZe4

==References==

http://chemwiki.ucdavis.edu/Physical_Chemistry/Thermodynamics/Laws_of_Thermodynamics/Second_Law_of_Thermodynamics

https://www.asme.org/engineering-topics/articles/energy/nicolas-leonard-sadi-carnot

http://physics.stackexchange.com/questions/113847/principle-of-caratheodory-and-the-second-law-of-thermodynamics

http://digital.nls.uk/scientists/biographies/lord-kelvin/

http://www.eoht.info/page/Caratheodory’s+theorem

http://chemwiki.ucdavis.edu/Physical_Chemistry/Thermodynamics/State_Functions/Entropy

http://www.panspermia.org/seconlaw.htm

http://www.theguardian.com/science/2013/dec/01/what-is-the-second-law-of-thermodynamics

https://www.quora.com/Given-that-it-costs-energy-to-desalinate-water-is-there-any-way-to-release-energy-in-a-usable-form-by-resalinating-it

http://www.learnthermo.com/examples/example-problem.php?ch=7&lesson=A&problem=1

http://entropysimple.oxy.edu/content.htm

[[Category:Energy]]

Second Law of Thermodynamics and Entropy

2017-03-27T08:30:20Z

Ezhao7:

Alyssa Candelmo (acandelmo6)
Edwin Zhao (ezhao7) Spring 17

==The Main Idea==

Entropy represents the quantity of the unavailability of a systems thermal energy to be converted into mechanical work. The entropy of the system can also be described as the systems level of disorder or randomness. The more entropy a system has, the more random it will be. The second law of thermodynamics states that the entropy of the universe will always increase over time. The second law also states that change in the entropy of the universe will never be negative. Essentially, through the discovery that heat can not spontaneously flow from a colder body to a hotter body, physicists also discovered that is impossible to complete any physical process without the loss of some useable energy. As time goes on, randomness can only increase.

[[File:Entropy.gif|center|border]]

==A Mathematical Model==

''Boltzmann's Equation: '''''ΔS'' = K ''lnΩ''''' ''

: Where ΔS is the change in entropy of the system

: ''K'' is the Boltzmann's Constant (or 1.38065 × 10‾²³ J/K)

: Ω is the number of microstates corresponding to a given macro state

''The Second Law of Thermodynamics: '''ΔS = ΔQ/T'', and ∫ΔQ/T ≤ 0'''

: Where ''ΔS'' is the change in entropy of the system

: ''ΔQ'' is the change in heat of the system,

: ''T'' is the temperature at the point where the heat transfer took place

==Example==

Considering the cycle made by taking path A followed by path B, using the given calculated integrals, determine if the cycle is reversible, irreversible, or impossible.

[[File:Cycle.png|right|border]]

[[File:I1.png|right|border]]

[[File:I2.png|right|border]]

We use the second law of thermodynamics and the Clausius inequality(∫ΔQ/T ≤ 0) to draw the conclusions that if the cyclic integral is:

*''Positive:'' the cycle is impossible

*''Negative:'' the cycle is irreversible

*''Zero:'' the cycle is reversible

[[File:I3.png]]

We use the equation above to include both paths in our cycle, and plug in their given values.

∫ΔQ/T = -27.7 + 41.3 = '''16.6'''

Because the value is > 0, we conclude that the cycle is impossible.

==Connectedness==

===How is this topic connected to something that you are interested in?===
For someone who loves to cook as much as I do, entropy plays a surprisingly large role. For example, entropy is the reason that Crystal Light power resolves in water. Over time, the particles spread and spread because the more spaced out they are, the more disorderly they are. And as we know, disorder must increase with time.

===How is it connected to your major?===

As an Industrial and Systems Engineering Major, a lot of the work I do will be designing production plants to be as efficient as they can possibly be. Understanding the concept of entropy and that no physical process can be completed without the loss of energy will help me to be able to account for that energy loss in my plans so that I can minimize the amount of inefficiency that occurs because of it. To understand that disorder is inherently more probable than order can help me be aware of more possible outcomes.

===Is there an interesting industrial application?===

The second law of thermodynamics is especially used in any industry making insulted products. Well, it is not "used" so much as it is fought against. Using the specifics of the second law of thermodynamics, companies who make thermos' or lunch boxes or insulation need to understand entropy and the second law to learn how to best fight heat dissipation so that they can keep hot things hot and cold thing cold.

==History==

===Contributors in the Development of the Second Law:===
[[File:Carnot.jpg|thumb|90px|Nicholas Carnot]]
*'''Nicholas Léonard Sadi Carnot''' (1 June 1796 – 24 August 1832)
**Considered to be the father of Thermodynamics
**Major Scientific Contributions:
***Carnot heat engine
***Carnot theorem
***Carnot efficiency
**His research was centered around learning if the work available from a heat source was limited, and whether the efficiency of a heat engine could be improved upon by replacing steam with a different substance
[[File:Clausius.jpg|thumb|90px|Rudolf Clausius]]
*'''Rudolf Clausius''' ( 2 January 1822 – 24 August 1888)
**German Physicist
**Developed the Clausius statement, which states that in general, heat can not flow spontaneously from a low temperature to a high temperature
**Wrote a famous paper titled "On the Moving Force of Heat and the Laws of Heat which May be Deduced Therefrom"
***Pointed out differences between the concept of conservation of energy
***Stated that assumptions about the Caloric theory were incorrect
**Presented the idea of Entropy and named it as such
**Was known for taking a mathematical approach to physics
[[File:Thompson.jpg|thumb|90px|William Thompson]]
*'''William Thompson''' (26 June 1824 – 17 December 1907)
**Also known as First Baron Kelvin
**Mathematical physicist and engineer
**Formulated the Kelvin Statement, which states that there is no way to convert all of the energy in a given system into work without losing energy
**Developed the vortex theory of the atom
**In addition to his contributions to thermodynamics, he also created the Kelvin scale
[[File:Caratheodory.jpg|thumb|90px|Constantin Caratheodory]]
*'''Constantin Carathéodory''' (13 September 1873 – 2 February 1950)
**German mathematician of Greek origin
**Principle of Caratheodory
**Took on thermodynamics with a mathematical axiomatic foundation
**Created his own version of the Second Law of Thermodynamics by stating that "In the neighborhood of any initial state, there are states which cannot be approached arbitrarily close through adiabatic changes of state."
**Used differential equations and Pfaffian expressions to prove the existence of entropy

== See also ==
[[The Energy Principle]]

[[Conservation of Energy]]

[[Thermal Energy]]

[[Energy Transfer due to a Temperature Difference]]

[[Work]]

==Further reading==

http://web.ist.utl.pt/berberan/data/68.pdf

https://www.youtube.com/watch?v=ByA_TBfMZe4

==References==

http://chemwiki.ucdavis.edu/Physical_Chemistry/Thermodynamics/Laws_of_Thermodynamics/Second_Law_of_Thermodynamics

https://www.asme.org/engineering-topics/articles/energy/nicolas-leonard-sadi-carnot

http://physics.stackexchange.com/questions/113847/principle-of-caratheodory-and-the-second-law-of-thermodynamics

http://digital.nls.uk/scientists/biographies/lord-kelvin/

http://www.eoht.info/page/Caratheodory’s+theorem

http://chemwiki.ucdavis.edu/Physical_Chemistry/Thermodynamics/State_Functions/Entropy

http://www.panspermia.org/seconlaw.htm

http://www.theguardian.com/science/2013/dec/01/what-is-the-second-law-of-thermodynamics

https://www.quora.com/Given-that-it-costs-energy-to-desalinate-water-is-there-any-way-to-release-energy-in-a-usable-form-by-resalinating-it

http://www.learnthermo.com/examples/example-problem.php?ch=7&lesson=A&problem=1

http://entropysimple.oxy.edu/content.htm

[[Category:Energy]]