Chapter 5.7, Problem 10P

(A)

Interpretation Introduction

Interpretation:

The temperature, pressure, fraction of vapor leaving the expansion valve, coefficient of performance and the mass flow rate.

Concept Introduction:

The energy balance equation for a reversible compressor is,

$\frac{{\dot{W}}_{S,rev}}{\dot{m}}={\widehat{H}}_{out,rev}-{\widehat{H}}_{in}$

The efficiency of the cycle is,

$\eta =\frac{\frac{{\dot{W}}_{S,rev}}{\dot{m}}}{\frac{{\dot{W}}_{S,act}}{\dot{m}}}$

Here, actual rate of work done by the shaft is ${\dot{W}}_{S,act}$.

The actual specific enthalpy by closing the energy balance is,

${\widehat{H}}_{out,act}={\widehat{H}}_{in}+\frac{{\dot{W}}_{S,act}}{\dot{m}}$

The expression to obtain the fraction of vapor in the stream leaving the expansion valve is,

${\widehat{H}}_{in}=q{\widehat{H}}_V+\left(1-q\right){\widehat{H}}_L$

Here, liquid phase and vapor phase specific enthalpy is ${\widehat{H}}_L$ and ${\widehat{H}}_V$ respectively.

The energy balance equation for the boiler is,

$\frac{{\dot{Q}}_C}{\dot{m}}={\widehat{H}}_{out}-{\widehat{H}}_{in}$

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

The expression to obtain the coefficient of performance is,

$\text{C}\text{.O}\text{.P}=\frac{\frac{{\dot{Q}}_C}{\dot{m}}}{\frac{{\dot{W}}_{S,act}}{\dot{m}}}$

(B)

Interpretation Introduction

Interpretation:

The temperature, pressure, fraction of vapor leaving the expansion valve, coefficient of performance and the mass flow rate.

Concept Introduction:

The energy balance equation for a reversible compressor is,

$\frac{{\dot{W}}_{S,rev}}{\dot{m}}={\widehat{H}}_{out,rev}-{\widehat{H}}_{in}$

The efficiency of the cycle is,

$\eta =\frac{\frac{{\dot{W}}_{S,rev}}{\dot{m}}}{\frac{{\dot{W}}_{S,act}}{\dot{m}}}$

Here, actual rate of work done by the shaft is ${\dot{W}}_{S,act}$.

The actual specific enthalpy by closing the energy balance is,

${\widehat{H}}_{out,act}={\widehat{H}}_{in}+\frac{{\dot{W}}_{S,act}}{\dot{m}}$

The expression to obtain the fraction of vapor in the stream leaving the expansion valve is,

${\widehat{H}}_{in}=q{\widehat{H}}_V+\left(1-q\right){\widehat{H}}_L$

Here, liquid phase and vapor phase specific enthalpy is ${\widehat{H}}_L$ and ${\widehat{H}}_V$ respectively.

The energy balance equation for the boiler is,

$\frac{{\dot{Q}}_C}{\dot{m}}={\widehat{H}}_{out}-{\widehat{H}}_{in}$

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

The expression to obtain the coefficient of performance is,

$\text{C}\text{.O}\text{.P}=\frac{\frac{{\dot{Q}}_C}{\dot{m}}}{\frac{{\dot{W}}_{S,act}}{\dot{m}}}$