Chapter 6.6, Problem 29P

Interpretation Introduction

Interpretation:

The change in Helmholtz energy when the gas is compressed isothermally has to be determined.

Concept introduction:

Fundamental property relation of molar Helmholtz energy $\left(\underset{\_}{A}\right)$:

$d\underset{\_}{A}=-Pd\underset{\_}{V}-\underset{\_}{S}dT$        (1)

Here, pressure is P, change in the temperature is dT, change in molar volume is $\underset{\_}{V}$, and molar entropy is $\underset{\_}{S}$.

The expansion rule:

${\left(\frac{\partial X}{\partial Y}\right)}_Z={\left(\frac{\partial X}{\partial K}\right)}_L{\left(\frac{\partial K}{\partial Y}\right)}_Z+{\left(\frac{\partial X}{\partial L}\right)}_K{\left(\frac{\partial L}{\partial Y}\right)}_Z$

Here, expansion rule parameters are $X,Y,K,\text{and}L$.