Chapter 4.7, Problem 2E

(A)

Interpretation Introduction

Interpretation:

The change in entropy for the system

Concept Introduction:

Write the expression to calculate the work done on contraction process.

$\begin{array}{l}{W}_{EC}=-Q\\ Q=P\left(V_2-V_1\right)\\ Q=PM\left({\widehat{V}}_{2@300°\text{C}}^V-{\widehat{V}}_{1@1\text{bar}}^V\right)\end{array}$

Here, initial volume and final volume is $V_1$ and $V_2$, specific volume for final and initial state is ${\widehat{V}}_2$ and ${\widehat{V}}_1$, system pressure is P, and mass of the system is M.

Write the expression to calculate the change in entropy for a system.

$S_2-S_1=\frac{Q_{rev}}{T}$

Here, final and initial entropy is $S_2\text{and}{S}_1$, heat energy added to the system on a reversible path is $Q_{rev}$, and the absolute temperature of the system at the boundary where the heat transfer occurs is T.

(B)

Interpretation Introduction

Interpretation:

The change in entropy for the system

Concept Introduction:

Write the expression to calculate the work done on contraction process.

$\begin{array}{l}{W}_{EC}=-Q\\ Q=P\left(V_2-V_1\right)\\ Q=PM\left({\widehat{V}}_{2@5\text{bar}}^L-{\widehat{V}}_{@5\text{bar},300°\text{C}}\right)\end{array}$

Here, initial volume and final volume is $V_1$ and $V_2$, specific volume for final and initial state is ${\widehat{V}}_2{}^L$ and ${\widehat{V}}_1$, system pressure is P, and mass of the system is M.

Write the expression to calculate the change in entropy for a system.

$S_2-S_1=\frac{Q_{rev}}{T}$

Here, final and initial entropy is $S_2\text{and}{S}_1$, heat energy added to the system on a reversible path is $Q_{rev}$, and the absolute temperature of the system at the boundary where the heat transfer occurs is T.

(C)

Interpretation Introduction

Interpretation:

The change in entropy for the system

Concept Introduction:

Write the expression to calculate the change in molar internal energy for an ideal gas.

$d\underset{\_}{U}=C_V^{*}\left(T_2-T_1\right)$

Here, constant volume for an ideal gas is $C_V^{*}$, temperature for inlet and exit state is $T_1$, and $T_2$ respectively.

Write the energy balance equation in terms of moles using first law of thermodynamics.

$N\left(d\underset{\_}{U}\right)=W_{EC}+Q$

Here, number of moles in the system is N.

Write the work expansion or contraction through the ideal gas law.

$W_{EC}=-NRT\ln \left(\frac{P_1}{P_2}\right)$

Here, initial and final pressure are $P_1$ and $P_2$ respectively.

(D)

Interpretation Introduction

Interpretation:

The change in entropy for the system

Concept Introduction:

Write the expression to calculate the change in molar internal energy for an ideal gas.

$d\underset{\_}{U}=C_V^{*}\left(T_2-T_1\right)$

Here, constant volume for an ideal gas is $C_V^{*}$, temperature for inlet and exit state is $T_1$, and $T_2$ respectively.

Write the energy balance equation in terms of moles using first law of thermodynamics.

$N\left(d\underset{\_}{U}\right)=W_{EC}+Q$

Here, number of moles in the system is N.

Write the work expansion or contraction through the ideal gas law.

$W_{EC}=-NRT\ln \left(\frac{P_1}{P_2}\right)$

Here, initial and final pressure are $P_1$ and $P_2$ respectively.