Question
Problem 1: Maxwell relations
a) Functions encountered in physics are generally well enough behaved that their mixed partial
derivatives do not depend on which derivative is taken first. For instance,
-P =
aslvN
S,N
Using the smoothness assumption, we find
д гди-
where each
av
is taken with S fixed, each
is taken with V fixed, and N is always held fixed.
From the thermodynamic identity (for U) you can evaluate the partial derivatives in parentheses
a nontrivial identity called a Maxwell relation. Go through the derivation of this relation step
by step.
Derive each Maxwell relation for the thermodynamic identities discussed in the text (for
U,H,F,G, not necessarily in this order), as shown below:
a)
lav
S,N
as/y.N
b)
s/ P.N
N*()
d) - (),
c)
ат/у
av
ат/ р N
You might find the following equations helpful:
dU = TdS – PdV + µdN
dF = -SdT – PdV + µdN
dG = -SdT + VdP + µdN
dH = TdS + VdP + µdN
expand button
Transcribed Image Text:Problem 1: Maxwell relations a) Functions encountered in physics are generally well enough behaved that their mixed partial derivatives do not depend on which derivative is taken first. For instance, -P = aslvN S,N Using the smoothness assumption, we find д гди- where each av is taken with S fixed, each is taken with V fixed, and N is always held fixed. From the thermodynamic identity (for U) you can evaluate the partial derivatives in parentheses a nontrivial identity called a Maxwell relation. Go through the derivation of this relation step by step. Derive each Maxwell relation for the thermodynamic identities discussed in the text (for U,H,F,G, not necessarily in this order), as shown below: a) lav S,N as/y.N b) s/ P.N N*() d) - (), c) ат/у av ат/ р N You might find the following equations helpful: dU = TdS – PdV + µdN dF = -SdT – PdV + µdN dG = -SdT + VdP + µdN dH = TdS + VdP + µdN
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