Chapter 6.6, Problem 12P

A)

Interpretation Introduction

Interpretation:

The expression for relating ${(dH/dV)}_T$  to measurable properties

Concept introduction:

The fundamental property of $\underset{\_}{H}$.

$d\underset{\_}{H}=Td\underset{\_}{S}+\underset{\_}{V}dP$

Here, molar enthalpy is $\underset{\_}{H}$, change in molar enthalpy is $d\underset{\_}{H}$, temperature is T, change in molar entropy is $d\underset{\_}{S}$, molar volume is $\underset{\_}{V}$, and change in pressure is dP.

Maxwell’s equation:

${\left(\frac{\partial \underset{\_}{S}}{\partial \underset{\_}{V}}\right)}_T={\left(\frac{\partial P}{\partial T}\right)}_{\underset{\_}{V}}$

Change in molar entropy with respect to change in molar volume at constant temperature is ${\left(\frac{\partial \underset{\_}{S}}{\partial \underset{\_}{V}}\right)}_T$ and change in pressure with respect to change in molar volume at constant temperature is ${\left(\frac{\partial P}{\partial T}\right)}_{\underset{\_}{V}}$.

Write the relationship between the gas constant and molar volume.

${\left(\frac{\partial P}{\partial T}\right)}_{\underset{\_}{V}}=\frac{R}{\underset{\_}{V}}$

B)

Interpretation Introduction

Interpretation:

Change in molar enthalpy of the gas has to be determined.

Concept introduction: