Chapter 3.9, Problem 21P

(A)

Interpretation Introduction

Interpretation:

Determine the fraction of initial contents $\left(q_{in}\right)$ of the vessel were in the vapor phase

Concept Introduction:

The expression to calculate the initial specific volume $\left({\widehat{V}}_{in}\right)$ of vessel.

${\widehat{V}}_{in}=\frac{V}{M_{in}}$

Here, volume of vessel is $V$ and initial mass in vessel is $M$.

The expression to calculate the fraction of initial contents $\left(q_{in}\right)$ of the vessel were in the vapor phase.

${\widehat{V}}_{in}=\left(1-q_{in}\right){\widehat{V}}^L+q_{in}{\widehat{V}}^V$

Here, specific volume in liquid phase is ${\widehat{V}}^L$ and specific volume in vapor phase is ${\widehat{V}}^V$.

(B)

Interpretation Introduction

Interpretation:

Determine the fraction of final contents $\left(q_{final}\right)$ of the vessel is in the vapor phase

Concept Introduction:

The expression to determine the final specific volume $\left({\widehat{V}}_{final}\right)$ of vessel.

${\widehat{V}}_{final}=\frac{V}{M}$

Here, volume of vessel is $V$, and total mass is $M$.

The expression to calculate the fraction of initial contents $\left(q_{in}\right)$ of the vessel were in the vapor phase.

${\widehat{V}}_{in}=\left(1-q_{in}\right){\widehat{V}}^L+q_{in}{\widehat{V}}^V$

Here, specific volume in liquid phase is ${\widehat{V}}^L$ and specific volume in vapor phase is ${\widehat{V}}^V$.

(C)

Interpretation Introduction

Interpretation:

Determine the heat removed $\left(Q\right)$ from the system

Concept Introduction:

The steady state energy balance equation for the heat exchanger.

$\Delta \left\{M\left(\widehat{U}+\frac{V^2}{2}+gh\right)\right\}=\left[\begin{array}{l}{\displaystyle \sum _{j=1}^{j=J}\left\{m_{j,in}\left({\widehat{H}}_j+\frac{V_j^2}{2}+g{h}_j\right)\right\}}\\ -{\displaystyle \sum _{k=1}^{k=K}\left\{m_{k,out}\left({\widehat{H}}_k+\frac{V_k^2}{2}+g{h}_k\right)\right\}}+W_{EC}+W_S+Q\end{array}\right]$

Here, total mass is $M$, specific internal energy is $\widehat{U}$, velocity is $V$, acceleration due to gravity is $g$, height is $h$, individual quantities of mass added to and removed from the process are $m_{j,in}\text{and}{m}_{k,out}$ respectively, initial specific enthalpy are ${\widehat{H}}_j$, final specific enthalpy is ${\widehat{H}}_k$, initial velocity is $V_j$, final velocity is $V_k$, initial height of the gas is $h_j$, final height of the gas is $h_k$, shaft work is added to the system is $W_{\text{S}}$, work is added to the system through expansion or contraction of the system is $W_{\text{EC}}$, and heat is added to the system is $Q$.

Write the expression to calculate the initial specific internal energy $\left({\widehat{U}}_{initial}\right)$.

${\widehat{U}}_{initial}=\left(1-q_{in}\right){\widehat{U}}^L+q_{in}{\widehat{U}}^V$

Here, specific internal energy in liquid phase is ${\widehat{U}}^L$, and specific internal energy in phase is ${\widehat{U}}^V$.