Chapter 3.9, Problem 22P

(A)

Interpretation Introduction

Interpretation:

The temperature of the water remaining in the vessel

Concept Introduction:

Write the steady state mass balance equation for the piston.

$M_2-M_1=-m_{out}$

Here, initial and final mass of a vessel is $M_1\text{and}{M}_2$, and mass removed out from the system is $m_{out}$.

Write the steady state energy balance equation for the piston.

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

Here, 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, individual quantities of mass added to and removed from the process are $m_{j,in}$ and $m_{k,out}$, specific enthalpies of streams inlet and outlet are ${\widehat{H}}_j$ and ${\widehat{H}}_k$, heights at which streams enters and leave the system are $h_j$ and $h_k$, total expansion or contraction work added throughout the process is $W_{EC}$, total shaft work added throughout the process is $W_S$, and the total heat added throughout the process is Q.

(B)

Interpretation Introduction

Interpretation:

The amount of water evaporated in order to cool the water remaining in the vessel to $25°\text{C}$.

Concept Introduction:

Write the steady state mass balance equation for the piston.

$M_2-M_1=-m_{out}$

Here, initial and final mass of a vessel is $M_1\text{and}{M}_2$, and mass removed out from the system is $m_{out}$.

Write the steady state energy balance equation for the piston.

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

Here, 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, individual quantities of mass added to and removed from the process are $m_{j,in}$ and $m_{k,out}$, specific enthalpies of streams inlet and outlet are ${\widehat{H}}_j$ and ${\widehat{H}}_k$, heights at which streams enters and leave the system are $h_j$ and $h_k$, total expansion or contraction work added throughout the process is $W_{EC}$, total shaft work added throughout the process is $W_S$, and the total heat added throughout the process is Q.

(C)

Interpretation Introduction

Interpretation:

The amount of water evaporated in order to cool the water remaining in the vessel $20°\text{C}$.

Concept Introduction:

Write the steady state mass balance equation for the piston.

$M_2-M_1=-m_{out}$

Here, initial and final mass of a vessel is $M_1\text{and}{M}_2$, and mass removed out from the system is $m_{out}$.

Write the steady state energy balance equation for the piston.

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

Here, 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, individual quantities of mass added to and removed from the process are $m_{j,in}$ and $m_{k,out}$, specific enthalpies of streams inlet and outlet are ${\widehat{H}}_j$ and ${\widehat{H}}_k$, heights at which streams enters and leave the system are $h_j$ and $h_k$, total expansion or contraction work added throughout the process is $W_{EC}$, total shaft work added throughout the process is $W_S$, and the total heat added throughout the process is Q.