Chapter 6.6, Problem 13P

A)

Interpretation Introduction

Interpretation:

The general expression for the residual molar enthalpy molar enthalpy has to be determined.

Concept introduction:

Write the general expression for the residual enthalpy $\left({\underset{\_}{H}}^R\right)$.

$\begin{array}{c}{\underset{\_}{H}}^R=\underset{\_}{H}-{\underset{\_}{H}}^{ig}\\ ={\displaystyle \underset{P=0,T=T}{\overset{P=P,T=T}{\int }}\left\{\underset{\_}{V}-T{\left(\frac{\delta \underset{\_}{V}}{\delta T}\right)}_P\right\}}dP\end{array}$

Here, molar enthalpy is $\underset{\_}{H}$, molar enthalpy for an ideal gas state is ${\underset{\_}{H}}^{ig}$, pressure is $P$, temperature is $T$, molar volume is $\underset{\_}{V}$, change in molar volume is $\delta \underset{\_}{V}$, change in temperature is $\delta T$, change in pressure is $dP$, change in molar volume and change in temperature at constant pressure is ${\left(\delta \underset{\_}{V}\right)}_P\text{and}{\left(\delta T\right)}_P$ respectively.

The compressibility factor $\left(Z\right)$ is given as follows.

$\begin{array}{c}Z=\frac{P\underset{\_}{V}}{RT}\\ Z=1+\frac{C{P}^2}{RT}\\ \underset{\_}{V}=\frac{RT}{P}+CP\end{array}$

Here, pressure is $P$, gas constant is $R$, and constant is $C$.

B)

Interpretation Introduction

Interpretation:

The general expression for the residual molar entropy has to be determined.

Concept introduction:

Write the expression for the residual molar entropy.

$\begin{array}{c}{\underset{\_}{H}}^R=\underset{\_}{S}-{\underset{\_}{S}}^{ig}\\ ={\displaystyle \underset{P=0,T=T}{\overset{P=P,T=T}{\int }}\left\{{\left(\frac{\delta \underset{\_}{V}}{\delta T}\right)}_P-\frac{R}{P}\right\}}dP\end{array}$

Here, molar entropy is $\underset{\_}{S}$, and molar entropy for an ideal gas state is ${\underset{\_}{S}}^{ig}$.

C)

Interpretation Introduction

Interpretation:

The change in molar enthalpy and entropy has to be determined.

Concept introduction:

The residual enthalpy formula for ideal gas has given as follows:

${\underset{\_}{H}}_2-{\underset{\_}{H}}_1=\left({\underset{\_}{H}}_2-{\underset{\_}{H}}_2{}^{ig}\right)+\left({\underset{\_}{H}}_2{}^{ig}-{\underset{\_}{H}}_1{}^{ig}\right)-\left({\underset{\_}{H}}_1-{\underset{\_}{H}}_1{}^{ig}\right)$

Here, inert gas molar enthalpy at state 1 and 2 is ${\underset{\_}{H}}_1{}^{ig}$ and ${\underset{\_}{H}}_2{}^{ig}$, gas molar enthalpy at state 1 and 2 is ${\underset{\_}{H}}_1$ and ${\underset{\_}{H}}_2$ respectively.

The expression for the change in molar enthalpy $\left(d\underset{\_}{H}\right)$ is given as follows

$d\underset{\_}{H}={\underset{\_}{H}}_2-{\underset{\_}{H}}_1$

Here, inert gas molar enthalpy at state 1 and 2 is ${\underset{\_}{H}}_1{}^{ig}$ and ${\underset{\_}{H}}_2{}^{ig}$

The change in molar entropy $\left(d\underset{\_}{S}\right)$ is given as follows:

$d\underset{\_}{S}=C_P^{\ast }\ln \left(T_2/T_1\right)+R\ln \left(P_1/P_2\right)$