Question

In: Chemistry

Show that Cp = T(∂S/∂T)p and Cv = T(∂S/∂T)V

Expert Solution

ANSWER:

Heat capacity:

It is a physical property of a matter, which can be calculated by the ratio of change in heat to the change in temperature. That is:

It is of two types:

At constant pressure (C_p); and
At constant volume (C_v).

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Now,

To prove:

Proof:

From thermodynamics:

dQ = TdS

From the formula of C_p:

From both equation:

(Proved)

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And,

To prove:

Proof:

From thermodynamics:

dQ = TdS

From the formula of C_v:

From both equation:

(Proved)

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queen_honey_blossom answered 2 years ago

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