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Thermodynamics Relations - Proof 10

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From the realtionships between specific heat and entropy, as given in
Equn.3.3 and Equn.4.4,

→ (10.1)
→ (10.2)
Therefore,

→ (10.3)
Considering *S* as a function of *T* & *V*, as

differentiating,

→ (10.4)
Dividing Equn.10.4 by *dT* at constant *P*,

i.e.,

→ (10.5)
By Maxwell relation 2,

Therefore,

→ (10.6)
**Cyclic relation rule:** (for the function in the variables
*x*, *y* & *z*)

→ (10.7)
We can write similar relation for the function in the variables
*P*, *T* & *V* as

→ (10.8)
i.e.,

→ (10.9)
and

→ (10.10)
Therefore,

→ (10.11)
Substituting for
from Equn.10.11 in Equn.10.6,

→ (10.12)
Substituting from Equn.10.12, in Equn.10.3,

→ (10.13)

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Last Modified on: 04-Feb-2022

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