$-12°C$ needs a condenser temperature of 28°C. The refrigerant $NH_3$ is subcooled by $5°C$ before entering the expansion valve. The vapour is 0.95 dry when it leaves the evaporator. Using P-H chart of $NH_3$ find (1) condition of refrigerant at outlet of compressor and at inlet to evaporator (2) COP and (3) Power required.

$T_E=T_{sat_{Pe}}=-12℃,T_C=T_{sat_{Pc}}$=28℃

Capacity=10 TR, x1=0.95

$h1=h_{f_{-12℃}}+ x1×h_{fg_{-12℃}}$

$h_{fg_{-12℃}}=h_g-h_f=1447.74-144.929$

=$1302.811 \frac{kJ}{kg} (from \ psychrometric \ chart \ booklet \ for \ N_3 )$

$h1=144.929+0.95×1302.811$

$=1382.6\frac{kJ}{kg}$

Now mark point 1 on p-h chart of ammonia corresponding to -12°C and h1. Then draw constant entropy line from point 1upwards to intersect horizontal line of 28°C. This is point 2. Draw a horizontal from this point towards left and where this line intersects constant temperature line of 23°C in subcooled region is point 3.

Condition of refrigerant at outlet of compressor i.e. point 2

$T2=67°C, h2=1598 kJ/kg, v2=0.15 m3/kg, P2=10.5 \ bar$

Condition of refrigerant at inlet to evaporator i.e. point 4

$T4=-12°C, h4=310 kJ/kg, P4=2.65$ bar

COP of given system = $\frac{R.E.}{Wc}=\frac{h1-h4}{h2-h1}$

COP=4.98

Also, $Q ̇_a=m ̇_R×(h1-h4)$

For 10 TR capacity, $10 x 3.5= m ̇_R×(1382.6-310)$

mass flow rate,$m ̇_R=0.0326 \frac{kg}{sec}$

Now, power required = $m ̇_R×(h2-h1)$

∴power required=7.0287 kW