Problem #$2(10$ pts$)$

A refrigeration system for a freezer uses R$-134$a$.$

The compressor isentropic efficiency is $75\%.$

The R$-134$a enters the compressor at state $1$ as a superheated vapor at $-10C$ and $0\mathrm{.}14$ MPa $(1\mathrm{.}4$ bar $).$

The pressure out of the compressor $($and into the condenser$)$ at state $2$ is $0\mathrm{.}9$ MPa $(9$ bar $).$

At state $3,$ the R $-134$a exits condenser $($and enters the throttling valve$)$ at state $3$ as a saturated liquid with $P_3=P_2.$

After going through the expansion valve from state $3$ to state $4($ so ${?}_{h_3}=h_4),$ the $R-134$ a is heated isobarically back to state $1.$

The freezer is at $-8C(T_L)$ and the kitchen it's in is at $25C(T_H)$

The heat removed from the freezer $(Q_L^{})$ is $20$ kW

Determine the following:

The $|\frac{W^{}}{m^{}}|$ for the compressor

The coefficient of performance $()$

The theoretical ${}_{\text{m}\text{a}\text{x}}$ if the freezer is at $-8C$ and the kitchen it's in is at $25C$

The mass flow rate of R$-134$a necessary remove $20$ kW of heat $(Q_L^{})$ from the freezer

The maximum temperature and minimum temperature that occur in this system $($hint: drawing the T$-$s diagram might help$)$

Plot the cycle on a T$-$s diagram