Chapter 6.6, Problem 11P

A)

Interpretation Introduction

Interpretation:

Determine $Q,W,\Delta U,\Delta H,\text{and }\Delta S$ for the ideal gas.

Concept introduction:

Consider the given gas as ideal gas and given process as isothermal process to obtain the $Q,W,\Delta U,\Delta H,\text{and }\Delta S$ fort the given gas.

Write the ideal gas equation as given as follows:

$PV=NRT$

Here, number of moles is $N$, volume is $V$, gas constant is R, and temperature is $T$.

The expression for the compression work $\left(W_{EC}\right)$ is given as follows.

$W_{EC}=-{\displaystyle \underset{V_1}{\overset{V_2}{\int }}PdV}$

Here, constant pressure is P, initial and final volume is $V_1\text{and}{V}_2$ respectively.

The energy balance equation for the closed system.

$U_2-U_1=Q+W_{EC}$

Here, final internal energy is $U_2$, initial internal energy is $U_1$, change in internal energy is $\Delta U$, and energy added or removed to the system is $Q$.

The expression for  the change in molar entropy is given as follows:

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

Here, constant pressure heat capacity for ideal gas is $C_P^{\ast }$, initial temperature is $T_1$, and final temperature is $T_2$.

B)

Interpretation Introduction

Interpretation:

Determine $Q,W,\Delta U,\Delta H,\text{and }\Delta S$ for the gas follows the van der Walls equation.

Concept introduction:

The given gas is follows the van der Walls equation so its follow the equation of state as given as follows:

$P=\frac{RT}{\underset{\_}{V}-b}-\frac{a}{{\underset{\_}{V}}^2}$

Using the fundamental of property relationship, total derivative relationship in the equation of state to obtain the value of $Q,W,\Delta U,\Delta H,\text{and }\Delta S$ for the given gas