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onye nkusi

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**Maxwell Relations - derivations**

## Homework Statement

1. Derive the Maxwell Relation based on the enthalpy.

2. Derive the Maxwell Relation based on the entropy.

## Homework Equations

H=U+PV

dU=dq+dw

dw=-PdV

dS=dq/T

## The Attempt at a Solution

1. I feel like I've gotten this one, but my final may or may not be off.

H=U+PV

dH=dU-d(PV)

dU=dq+dw --- dS=dq/T --- dw=-PdV

dU=TdS-PdV

dH=TdS-PdV+PdV+VdP --- This part I'm unsure about.

dH=TdS+VdP

Finally... (δT/δP)s=-(δV/δS)p

2.

dS=dq/T

TdS=dq

(δT/δq)s=(X/δS) --- I'm absolutely stuck here.

Any input you guys have for either problem, especially the second, is highly appreciated. Thanks.

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