Past exam of the mathematics course of the University of Cambridge / 2015 / ii / Paper 3 / 33C / a / ii

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- Solution ii

Solution

The heat capacity at constant pressure is

C_{p} = (δ Q / \partial T)_{p} = T (\partial S / \partial T)_{p}

for reversible heat input. The enthalpy is

H = U + p V

, so

d H = T d S + V d p

. Along an isobar this gives $C_{p} = (\partial H / \partial T)_{p}$ .

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