|
|
| (44 intermediate revisions by 3 users not shown) |
| Line 1: |
Line 1: |
| by Dejan Tojcic
| |
|
| |
|
| ==Specific Heat Capacity ==
| |
|
| |
| Specific Heat Capacity is simply a physical quantity that represents the ratio of the amount of heat taken or added to substance or object which results in a temperature change. The formal definition of Specific Heat is the amount of heat required to raise the temperature of 1 gram of a substance 1°C. The Standard Unit(SI) of this quantity is, joule per celsius per kilogram or or <math>\mathrm{\tfrac{J}{°C*Kg}}</math>. Different objects/substances have different specific heat capacities because every object has a varying mass, molecular structure, and numbers of particles per unit mass specific, and since specific heat capacity is reliant on mass, every different object has a different specific heat capacity.
| |
|
| |
| [[File:specificheatmetals.jpg]]
| |
|
| |
| ===A Mathematical Model===
| |
|
| |
| In order to find the Specific Heat Capacity of a substance, we use the equation:<math> \Delta E_{\mathrm{thermal}} = C * M * \Delta T </math>, and rearrange it to get <math> C= \Delta E_{\mathrm{thermal}} /( M * \Delta T) .</math> where ''C'' is the Specific Heat Capacity with units of joules per celsius per kilogram or <math>\mathrm{\tfrac{J}{°C*Kg}}</math>, ''M'' is the mass measured in kilograms or <math>\mathrm{kg}</math>, ''<math> \Delta E_{\mathrm{thermal}} </math>'' represents the change in thermal energy measured by joules or <math>\mathrm{J}</math>, and ''<math> \Delta T </math>'' represents change in temperature with units celsius or <math>\mathrm{°C.}</math>
| |
|
| |
|
| |
| [[File:picture2.jpg]]
| |
|
| |
| ===A Computational Model===
| |
|
| |
| How do we visualize or predict using this topic. Consider embedding some vpython code here [https://trinket.io/glowscript/31d0f9ad9e Teach hands-on with GlowScript]
| |
|
| |
| =Simple Example=
| |
|
| |
| '''''Question'''''
| |
| It takes 487.5 J to heat 25 grams of copper from 25 °C to 75 °C. What is the specific heat in Joules/g·°C?
| |
|
| |
| [[File:Zvezda33.jpg]]
| |
|
| |
|
| |
| ----
| |
|
| |
| '''''Solution'''''
| |
|
| |
| This problem is very simplistic in nature as we are simply need to plug all of the values into the equation.
| |
| Remembering the equation
| |
|
| |
|
| |
| [[File:Zvezda5.jpg]]
| |
|
| |
|
| |
| All we have to do is rearrange it and solve for the specific heat capacity
| |
|
| |
|
| |
| [[File:zvezda6.jpg]]
| |
|
| |
|
| |
| Knowing that ''<math> \ Q </math>'' or ''<math> \Delta E_{\mathrm{thermal}} </math>'' is equal to the change in thermal energy, we can plug in ''487.5 Joules'' into the equation, so now we have
| |
|
| |
|
| |
| <math> C= 487.5 joules /( M * \Delta T) .</math>
| |
|
| |
|
| |
| Next, looking at the question it looks like we are given the mass or <math>\mathrm{M}</math> which is ''25 grams'' or . And can now plug that into the equation to get
| |
|
| |
|
| |
| <math> C= 487.5 joules /(25g * \Delta T) .</math>
| |
|
| |
|
| |
| Lastly, when we read the problem we see that we are given ''<math> \Delta T </math>'' which in this case would be <math> (75 °C-25 °C) </math> or <math> 50 °C </math>. We can finally solve for the value of <math>\mathrm{C}</math> which is
| |
|
| |
| <math> C= 487.5 joules /( 25g * 50 °C) .</math>
| |
|
| |
|
| |
| and we finally conclude that
| |
|
| |
|
| |
| <math> C= .39{\tfrac{J}{g*°C}}</math> or the specific heat of copper is .39 J/(g*°C).
| |
|
| |
|
| |
|
| |
|
| |
|
| |
|
| |
|
| |
| =Intermediate example=
| |
|
| |
| '''''Question''''' What is the final temperature when 625 grams of water at 75.0° C loses 7.96 x 10^4 J?
| |
|
| |
| [[File:zvezda7.jpg]]
| |
|
| |
|
| |
|
| |
| ----
| |
|
| |
| '''Solution'''
| |
| While this problem may seem impossible at first glance, it really is not. It appears as if we are missing two constants,<math>\Delta T </math> and <math>C </math>, or change in temperature and specific heat capacity. Water's specific heat capacity is almost "a universal constant" as it is noted for being the highest out of all substances with the value of 4.18 joules/(grams* °C). Now knowing the value <math>C=4.18{\tfrac{J}{°C*g}} </math>, we see that the question is asking for <math>\Delta T </math>, which is equal to <math>( T_{\mathrm{final}} - T_{\mathrm{initial}})</math>.
| |
|
| |
| [[File:Zvezda5.jpg]]
| |
|
| |
|
| |
| We can again use the same equation as on this occasion we are solving for <math>\Delta T </math> or <math>( T_{\mathrm{final}})</math> more specifically, so we can rearrange it to get
| |
|
| |
|
| |
|
| |
| <math>\Delta T= \Delta E_{\mathrm{thermal}}/( C * M)</math>
| |
|
| |
|
| |
|
| |
|
| |
|
| |
| =Hard Example=
| |
|
| |
|
| |
|
| |
|
| |
|
| |
| =Connectedness=
| |
| #How is this topic connected to something that you are interested in?
| |
| #How is it connected to your major?
| |
| #Is there an interesting industrial application?
| |
|
| |
| ==History==
| |
|
| |
| Put this idea in historical context. Give the reader the Who, What, When, Where, and Why.
| |
|
| |
| == See also ==
| |
|
| |
| Are there related topics or categories in this wiki resource for the curious reader to explore? How does this topic fit into that context?
| |
|
| |
| ===Further reading===
| |
|
| |
| Books, Articles or other print media on this topic
| |
|
| |
| ===External links===
| |
|
| |
| Internet resources on this topic
| |
|
| |
| ==References==
| |
|
| |
| This section contains the the references you used while writing this page
| |
|
| |
| [[Category:Which Category did you place this in?]]
| |