Chapter 4.8, Problem 28P

(A)

Interpretation Introduction

Interpretation:

To determine the mass of steam.

Concept Introduction:

The mass of steam using the relation specific volume and volume.

$m=\frac{V}{\widehat{V}}$

Here, specific volume is $\widehat{V}$ and volume is V.

(B)

Interpretation Introduction

Interpretation:

To determine the volume of the chamber that was initially evacuated.

Concept Introduction:

The steady state energy balance equation for the chambers.

$\frac{d}{dt}\left\{M\left(\widehat{U}+\frac{v^2}{2}+gh\right)\right\}=\left(\begin{array}{l}{\displaystyle \sum _{j=1}^{j=J}{\dot{m}}_{j,in}\left({\widehat{H}}_j+\frac{v_j^2}{2}+g{h}_j\right)}-{\displaystyle \sum _{k=1}^{k=K}{\dot{m}}_{k,out}\left({\widehat{H}}_k+\frac{v_k^2}{2}+g{h}_k\right)}\\ +{\dot{W}}_S+{\dot{W}}_{EC}+\dot{Q}\end{array}\right)$

Here, time taken is t, total mass of the system is M, specific internal energy of the system is $\widehat{U}$, velocity of the system is v, height of the system is h, acceleration due to gravity is g, mass flow rate for inlet and outlet streams is ${\dot{m}}_{j,in}$ and ${\dot{m}}_{k,out}$, specific enthalpies of streams inlet and outlet is ${\widehat{H}}_j$ and ${\widehat{H}}_k$, heights at which streams enters and leave the system is $h_j$ and $h_k$, rate at which work is added to the system through expansion or contraction of the system is ${\dot{W}}_{EC}$, rate at which shaft work is added to the system is ${\dot{W}}_S$, and the rate at which heat is added to the system is $\dot{Q}$.

(C)

Interpretation Introduction

Interpretation:

To determine the change in entropy of the universe.

Concept Introduction:

The general expression for an entropy balance equation.

$\frac{d\left(M\widehat{S}\right)}{dt}={\displaystyle \sum _{j=1}^{j=J}{\dot{m}}_{j,in}{\widehat{S}}_j}-{\displaystyle \sum _{k=1}^{k=K}{\dot{m}}_{k,out}{\widehat{S}}_k}+{\displaystyle \sum _{n=1}^{n=N}\frac{{\dot{Q}}_n}{T_n}}+{\dot{S}}_{gen}$

Here, time taken is t, mass of the system is M, specific entropy of the system is $\widehat{S}$, mass flow rates of individual streams entering and leaving the system are ${\dot{m}}_{j,in}$ and ${\dot{m}}_{k,out}$, specific entropies of streams entering and leaving the system are ${\widehat{S}}_j$ and ${\widehat{S}}_k$, actual rate at which heat is added to or removed from the system at one particular location is ${\dot{Q}}_n$, the temperature of the system at the boundary where the heat transfer labeled n occurs is $T_n$, and the rate at which entropy is generated within the boundaries of the system is ${\dot{S}}_{gen}$.

(D)

Interpretation Introduction

Interpretation:

Determine the value entropy generation.

Concept Introduction:

Write the number of moles using the ideal gas law.

$n=\frac{PV}{RT}$

Here, pressure is P, volume is V, gas constant is R, and temperature is T.

Write the entropy difference between the two chambers.

$\begin{array}{c}{\underset{\_}{S}}_2-{\underset{\_}{S}}_1=C_V^{*}\ln \left(\frac{T_2}{T_1}\right)+R\ln \left(\frac{T_2{P}_1}{T_1{P}_2}\right)\\ =\left(C_P^{*}-R\right)\ln \left(\frac{T_2}{T_1}\right)+R\ln \left(\frac{T_2{P}_1}{T_1{P}_2}\right)\end{array}$

Here, initial and final pressure and temperature is $P_1,P_2,T_1,\text{and}{T}_2$, gas constant is R, constant pressure heat capacity on a gas basis is $C_P^{*}$.