?(a) Making use of the fact that Eq. (6.21) is an exact differential expression, show

Chapter 6, Problem 6.2

(choose chapter or problem)

(a) Making use of the fact that Eq. (6.21) is an exact differential expression, show that:

\(( ∂ C_{P} / ∂P )_{T} = − T ( ∂^{2} V / ∂ T^{2} )_{P}\)

What is the result of application of this equation to an ideal gas?

(b) Heat capacities \(C_{V}\) and \(C_{P}\) are defined as temperature derivatives respectively of U and H. Because these properties are related, one expects the heat capacities also to be related. Show that the general expression connecting \(C_{P}\) to \(C_{V}\) is:

\(C_{P} = C_{V} + T (\frac {∂P}{∂T})_{V} (\frac {∂V}{∂T})_{P}\)

Show that Eq. (B) of Ex. 6.2 is another form of this expression.

Text Transcription:

(∂ C_P / ∂P )_T = − T ( ∂^2 V / ∂ T^2 )_P

C_V

C_P

C_P = C_V + T (∂P/∂T)_V (∂V / ∂T)_P