Chapter 3.9, Problem 24P

(A)

Interpretation Introduction

Interpretation:

The work required to compress the vapor

Concept Introduction:

The steady state energy balance equation for compressor:

$\frac{d}{dt}\left\{M\left(\widehat{U}+\frac{v^2}{2}+gh\right)\right\}={\dot{m}}_{in}\left({\widehat{H}}_{in}+\frac{v_{in}^2}{2}+g{h}_{in}\right)-{\dot{m}}_{out}\left({\widehat{H}}_{out}+\frac{v_{out}^2}{2}+g{h}_{out}\right)+{\dot{W}}_S+{\dot{W}}_{EC}+\dot{Q}$

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

(B)

Interpretation Introduction

Interpretation:

The estimated work required to pump the liquid and the temperature of the existing fluid.

Concept Introduction:

The expression to determine the work required to compress the vapor.

$\frac{{\dot{W}}_S}{\dot{m}}=\widehat{V}\left(P_{out}-P_{in}\right)$

Here, specific volume is $\widehat{V}$, inlet and exit pressure is $P_{in}\text{and}{P}_{out}$ respectively.