2. Let A = A(T,V) and G = G(T,p) be thermodynamic state functions with total differentials dA = -SdT – pdV and dG = -SdT+V dp, where p, V, T, and S are, respectively, pressure, volume, temperature and entropy. a) Use dA and suitable relationships between partial derivatives to show that Cv dT + ()av dS (2) T av av as ƏT where a 1 1 and Cy = T K = V ƏT V

2. Let A = A(T,V) and G = G(T,p) be thermodynamic state functions with total differentials dA = -SdT – pdV and dG = -SdT+V dp, where p, V, T, and S are, respectively, pressure, volume, temperature and entropy. a) Use dA and suitable relationships between partial derivatives to show that Cv dT + ()av dS (2) T av av as ƏT where a 1 1 and Cy = T K = V ƏT V

Physics for Scientists and Engineers

10th Edition

ISBN:9781337553278

Author:Raymond A. Serway, John W. Jewett

Publisher:Raymond A. Serway, John W. Jewett

Chapter20: The Kinetic Theory Of Gases

Section: Chapter Questions

Problem 45CP

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Question

I need help with my problem. I do not know how to approach it. Show me detailed steps.

2. Let A = A(T,V) and G = G(T,p) be thermodynamic state functions with total
differentials dA = -SdT – pdV and dG = -SdT + V dp, where p, V, T, and S are,
respectively, pressure, volume, temperature and entropy.
a) Use dA and suitable relationships between partial derivatives to show that
Cv aT + ()av
dS
(2)
T
where a = +().,
÷(), and Cy = T()
1
1
K
ƏT
T
b) Use dG and suitable relationships between partial derivatives to show that
Cp
dT – aV dp
dS =
(3)
where C, = T().
as
ƏT
c) Use (2) and (3) and suitable relationships between partial derivatives to show that
Cp = Cy +TVª²
(4)
K
d) For a particular material, the values of Cp, a, and k as a function of tempera-
ture and pressure are readily available. A mole of this material is subjected to an
expansion process from V to V2 during which the temperature is observed to change
from T1 to T2 in a manner that depends with volume as T
constants to be determined). Use (2) and (4) to find an integral expression for the
change in entropy for this process, AS1→2 =
experimentally accessible quantities Cp, a, and K.
= a + bV (a and b are
S(T2, V2) – S(T1, Vị), in terms of the

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