Chapter 4.8, Problem 21P

(A)

Interpretation Introduction

Interpretation:

The heat is added to the boiler per kilogram $\left(\dot{Q}/\dot{m}\right)$ of entering Freon 22.

Concept Introduction:

Write the steady state energy balance equation for the boiler.

$\frac{d}{dt}\left\{M\left(\widehat{U}+\frac{V^2}{2}+gh\right)\right\}=\left[\begin{array}{l}{\dot{m}}_{in}\left({\widehat{H}}_{in}+\frac{V_{in}^2}{2}+g{h}_{in}\right)-{\dot{m}}_{out}\left({\widehat{H}}_{out}+\frac{V_{out}^2}{2}+g{h}_{out}\right)\\ +{\dot{W}}_{\text{S}}+W_{\text{EC}}+\dot{Q}\end{array}\right]$

Here, total mass is $M$, specific internal energy is $\widehat{U}$, velocity is $V$, time taken is $t$, acceleration due to gravity is $g$, height is $h$, initial mass flow rate is ${\dot{m}}_{in}$, initial specific enthalpy is ${\widehat{H}}_{in}$, initial velocity is $V_{in}$, initial height of the gas is $h_{in}$, final mass flow rate is ${\dot{m}}_{out}$, final height of the gas is $h_{out}$, rate at which shaft work is added to the system is ${\dot{W}}_{\text{S}}$, rate at which work is added to the system through expansion or contraction of the system is ${\dot{W}}_{\text{EC}}$, and rate at which heat is added to the system is $\dot{Q}$.

(B)

Interpretation Introduction

Interpretation:

The flow rate $\left(\dot{m}\right)$ of Freon through the boiler.

Concept Introduction:

Write the expression to determine the flow rate $\left(\dot{m}\right)$ of Freon through the boiler.

$\dot{m}=\dot{Q}\left(\frac{1}{\dot{Q}/\dot{m}}\right)$

Here, rate of heat addition is $\dot{Q}$.