2. (Kittel 6.5) Integration of the thermodynamic identity for an ideal gas. From the thermodynamic identity at a constant number of particles we have JU dU do = + T pdV T T dt+ Show by integration that for an ideal gas the entropy is o=C₂ log T+ Nlog V + 0₁ T where o, is a constant independent of 7 and V. T dV + pdV T
2. (Kittel 6.5) Integration of the thermodynamic identity for an ideal gas. From the thermodynamic identity at a constant number of particles we have JU dU do = + T pdV T T dt+ Show by integration that for an ideal gas the entropy is o=C₂ log T+ Nlog V + 0₁ T where o, is a constant independent of 7 and V. T dV + pdV T
Elements Of Electromagnetics
7th Edition
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Sadiku, Matthew N. O.
ChapterMA: Math Assessment
Section: Chapter Questions
Problem 1.1MA
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![**Integration of the Thermodynamic Identity for an Ideal Gas**
From the thermodynamic identity at a constant number of particles, we have:
\[
d\sigma = \frac{dU}{\tau} + \frac{pdV}{\tau} = \frac{1}{\tau} \left( \frac{\partial U}{\partial \tau} \right)_V d\tau + \frac{1}{\tau} \left( \frac{\partial U}{\partial V} \right)_\tau dV + \frac{pdV}{\tau}
\]
Show by integration that for an ideal gas the entropy is:
\[
\sigma = C_v \log \tau + N \log V + \sigma_1
\]
where \( \sigma_1 \) is a constant independent of \( \tau \) and \( V \).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F0d2fdd51-a813-4b36-89e9-f9581acfc2ee%2F21a555bc-7d16-4863-980d-a5a88d7519fc%2Fl6tstm_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Integration of the Thermodynamic Identity for an Ideal Gas**
From the thermodynamic identity at a constant number of particles, we have:
\[
d\sigma = \frac{dU}{\tau} + \frac{pdV}{\tau} = \frac{1}{\tau} \left( \frac{\partial U}{\partial \tau} \right)_V d\tau + \frac{1}{\tau} \left( \frac{\partial U}{\partial V} \right)_\tau dV + \frac{pdV}{\tau}
\]
Show by integration that for an ideal gas the entropy is:
\[
\sigma = C_v \log \tau + N \log V + \sigma_1
\]
where \( \sigma_1 \) is a constant independent of \( \tau \) and \( V \).
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