Suppose that S is regarded as a function of P and T. Show that TdS= CpdT- aTVdp.

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Suppose that S is regarded as a function of P and T. Show that TdS= CpdT- aTVdp. Hence, show that the energy transferred as heat when the pressure on an incompressible liquid or solid is increased by ∆p is equal to -aTV∆p.
Evaluate q when the pressure acting on 100 cm3 of mercury at O°C is increased by 1.0 kbar, (0:= 1.82 x 10-4 K-J.)
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