?Starting with Eq. (6.9), show that isotherms in the vapor region of a Mollier (HS)

Chapter 6, Problem 6.81

(choose chapter or problem)

Starting with Eq. (6.9), show that isotherms in the vapor region of a Mollier (HS) diagram have slopes and curvatures given by:

\((\frac {∂H}{∂S})_{T} = \frac {1}{β}(βT − 1)\)  \((\frac {∂^{2}H}{∂S^{2}})_{T}= −\frac {1}{β^{3}V} (\frac {∂β}{∂P})_{T}\)

Here, β is volume expansivity. If the vapor is described by the two-term virial equation in P, Eq. (3.36), what can be said about the signs of these derivatives? Assume that, for normal temperatures, B is negative and dB/dT is positive.

Text Transcription:

(∂H /∂S)_T = 1/β(βT − 1)

(∂^2H/∂S^2)_T= −1/β^3V} (∂β/∂P)_T