$($b$)$ In a refrigeration system utilizing Refrigerant$-22$ as the working fluid, an ideal vaporcompression refrigeration cycle operates between pressure levels of $131\mathrm{.}68$ kPa and $680\mathrm{.}7$ kPa $.$ If the system has a refrigerant mass flow rate of $0\mathrm{.}3k\frac{g}{s},$ calculate the following:

i$.$ The rate of heat extracted from the refrigerated space and the power required by the compressor.

ii$.$ The rate of heat dissipated to the surroundings.

iii. The Coefficient of Performance $($COP$)$ for the refrigerator.

$(15$ marks$)$

Refrigerant$-22$

mass flow rate $m^{}=0\mathrm{.}3k\frac{g}{s}$

The rate ul$\text{'}$ heal extracted Irum the relingerated spave

SFEE:

$Q^{}=m^{}(h_1-h_4)$

$=0\mathrm{.}3(390\mathrm{.}896-211\mathrm{.}877)$

$=53\mathrm{.}7k\frac{J}{s}$

Power required by the compressor

$dq-dw=dh+CdC+gdZ$

$dq-dw=dh+gdc+glL$

$dq-dw=dh+gc+gdL$

$-dw=dh$

$-w=m^{}(h2-h1)$

$=0\mathrm{.}3(412\mathrm{.}651-390\mathrm{.}896)$

$=6\mathrm{.}53k\frac{w}{2}$

$Q^{}=m^{}(h_2-h_3)$

$=0\mathrm{.}3(412\mathrm{.}61-211\mathrm{.}877)$

$=60\mathrm{.}2322$

iii. The Coefficient of Performance $($COP$)$ for the refrigerator.

$=\frac{53\mathrm{.}7}{6\mathrm{.}53}$

$=8\mathrm{.}22$