Chapter 6, Problem 6.81P

Interpretation Introduction

Interpretation:

Show that isotherms in the vapor region of a Mollier diagram have slopes and curvatures given by:

${\left(\frac{\partial H}{\partial S}\right)}_T=\frac{1}{\beta }\left(\beta T-1\right)$and${\left(\frac{{\partial }^{2}H}{\partial S^2}\right)}_T=-\frac{1}{{\beta }^{3}V}{\left(\frac{\partial \beta }{\partial P}\right)}_T$

If the vapor is described by the two-term virial equation in$P$, what can be said about the signs of these derivatives.

Concept Introduction:

Mollier diagram is the graphical representation of relationship between temperature, moisture content and enthalpy. It is enthalpy and entropy graph and hence it has slope$\left(\frac{\partial H}{\partial S}\right)$and curvature$\left(\frac{{\partial }^{2}H}{\partial S^2}\right)$.