Schaums Outline: Entropy Ques - Tmp Not Constant

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Discussion Overview

The discussion revolves around the application of the entropy equation (delta S = delta Q / T) in scenarios where temperature is not constant. Participants explore the implications of using an average temperature for calculations and the accuracy of such approximations.

Discussion Character

  • Technical explanation
  • Mathematical reasoning
  • Debate/contested

Main Points Raised

  • Some participants question the validity of using the equation delta S = delta Q / T when temperature is not constant, noting that it is treated as constant by taking an average temperature.
  • Others argue that using the mean temperature is an approximation that can be acceptable over small temperature changes, emphasizing the goal of demonstrating that total entropy increases.
  • A participant suggests that accurately calculating entropy change requires calculus, providing a detailed integral expression for delta S involving specific heat and temperature changes.
  • There is a clarification regarding the variables used, with one participant indicating that n1 refers to the number of moles of gas rather than mass, and discussing the appropriate units for specific heat.

Areas of Agreement / Disagreement

Participants express differing views on the appropriateness of using an average temperature for entropy calculations, indicating that multiple competing perspectives remain on this topic.

Contextual Notes

Participants note that the approximation of using mean temperature may depend on the size of the temperature change and that the discussion involves assumptions about the definitions of variables and units.

Who May Find This Useful

This discussion may be of interest to students and educators in physics, particularly those studying thermodynamics and entropy, as well as individuals seeking to understand the nuances of applying theoretical equations in practical scenarios.

p75213
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This question appears in "Schaums Outline of College Physics". Please click the link:

http://www.4shared.com/photo/jbJ3lZwT/ScreenHunter_01_Sep_04_1256.html"

My question is how can they use this equation (delta S=(delta Q)/T) when the temperature is not constant? They treat it as being constant by taking the average temp.
 
Last edited by a moderator:
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p75213 said:
This question appears in "Schaums Outline of College Physics". Please click the link:

http://www.4shared.com/photo/jbJ3lZwT/ScreenHunter_01_Sep_04_1256.html"

My question is how can they use this equation (delta S=(delta Q)/T) when the temperature is not constant? They treat it as being constant by taking the average temp.
It is just an approximation to use the mean temperature over such a small temperature change. The point is to show that total entropy increases.

To do it accurately involves a bit of calculus:

[tex]\Delta S_h = \int_{340}^{338} dS = \int_{340}^{338} dQ/T = \int_{340}^{338} n_1C_v dt/T = n_1C_v\ln\left(\frac{338}{340}\right) \approx n_1C_v\left(\frac{2}{339}\right)[/tex]

AM
 
Last edited by a moderator:
Thanks for the reply. I suspected that was the case.
 
Andrew Mason said:
It is just an approximation to use the mean temperature over such a small temperature change. The point is to show that total entropy increases.

To do it accurately involves a bit of calculus:

[tex]\Delta S_h = \int_{340}^{338} dS = \int_{340}^{338} dQ/T = \int_{340}^{338} n_1C_v dt/T = n_1C_v\ln\left(\frac{338}{340}\right) \approx n_1C_v\left(\frac{2}{339}\right)[/tex]

AM

Elegant. I assume n1 is the mass.
 
Last edited:
p75213 said:
Elegant. I assume n1 is the mass.
I intended n1 to be the number of moles of the gas in the first compartment and C_v to have units of J/mole K. I probably should have used m and Cv in units of J/kg K, since that is what is used in this example.

AM
 

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