Chapter 3, Problem 3.26NP

Interpretation Introduction

Interpretation:

For a gas which obeys the equation of state, $V_m=\frac{RT}{P}+B\left(T\right)$ , the result ${\left(\frac{\partial H}{\partial P}\right)}_T=B(T)-T\frac{dB(T)}{dT}$ needs to be derived.

Concept Introduction :

The relation $\left(\frac{\partial H}{\partial P}\right)=-T{\left(\frac{\partial V_m}{\partial T}\right)}_P+V_m$ is correct for a gas obeying $V_m=\frac{RT}{P}+B(T).$

Here,

V_m = molar volume of the gas

R = gas constant

P = pressure

T = absolute temperature

  $\partial H$ = enthalpy change

  $\partial P$ = pressure change

  $\partial T$ = temperature change