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Unformatted text preview: he results of the previous question, show that:
i.
ii.
iii.
iv.
v. Cp − CV = T
∂E
∂V
∂E
∂p
∂CV
∂V
∂Cp
∂p ∂V
∂T p ∂p
∂T V ∂p
−p
∂T V
∂V
∂V
= −T
−p
∂T p
∂p = −T =T T T 2 ∂p
∂T 2 V
T
∂2V
= −T
∂T 2 p
T
=T 1 T ∂V
∂T 2 p ∂p
∂V T 3. Consider a classical ideal gas with equation of state pV = NkB T and constant heat
capacity CV = NkB α for some α. Use the results above to show that Cp = NkB (α +1),
and that the entropy is
S = NkB log V
N + NkB α log T +...
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 Spring '14

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