Chapter 4.8, Problem 23P

(A)

Interpretation Introduction

Interpretation:

Determine the heat is removed from the condenser per kilogram $\left(\dot{Q}/\dot{m}\right)$ of entering Freon 22.

Concept Introduction:

The steady state energy equation for the condenser.

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

Here, time taken is $t$, total mass is $M$, specific internal energy is $\widehat{U}$, velocity is $V$, 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:

Determine the flow rate $\left(\dot{m}\right)$ of Freon in the condenser.

Concept Introduction:

Write the flow rate $\left(\dot{m}\right)$ of Freon in the condenser.

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

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

(C)

Interpretation Introduction

Interpretation:

Determine the change in entropy of the universe.

Concept Introduction:

Write an entropy balance for the coolant side only.

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

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

Write the entropy energy for the system.

$0={\dot{m}}_{Freon,in}{\widehat{S}}_{Freon,in}+{\dot{m}}_{coolant,in}{\widehat{S}}_{coolant,in}-{\dot{m}}_{Freon,out}{\widehat{S}}_{Freon,out}-{\dot{m}}_{coolant,out}{\widehat{S}}_{coolant,out}+{\dot{S}}_{gen}$

Here, initial mass flow rate of Freon in ${\dot{m}}_{Freon,in}$, initial specific entropy of Freon is ${\widehat{S}}_{Freon,in}$, initial mass flow rate of coolant is ${\dot{m}}_{coolant,in}$, initial specific entropy of coolant is ${\widehat{S}}_{coolant,in}$, final mass flow rate of Freon is ${\dot{m}}_{Freon,out}$, final specific entropy of Freon is ${\widehat{S}}_{Freon,out}$, final mass flow rate of coolant is ${\dot{m}}_{coolant,out}$, and final specific entropy of coolant is ${\widehat{S}}_{coolant,out}$.