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A refrigeration system using $NH$_3 works on standard vapour compression cycle.The condensing temperature

is $30°C$. investigate the performance of the system based on:-

i)COP

ii)Mass of refrigerant circulated

iii)Volume of refrigerant handled by compressor

iv)Temperature of refrigerant at compressor delivery. The system operates at temperature in the evaporator of -10°C and 16°C respectively. Capacity of the system is 10TR. Use properties of saturated $NH_3$ as:

Marks: 12M,

Year: Dec2014, Dec2015, Dec2013, May2014

Difficulty: Medium

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$T_E=T_{sat_{Pe}}=-10℃,T_C=T_{sat_{Pc}}=30℃$

Capacity = 10TR

∴$Q ̇_a=3.5×10=35 kJ/sec$

Assuming that superheating of refrigerant at inlet to compressor takes place in evaporator and adds to refrigeration effect.

s1=s2

$s_{g_{-10℃}}+Cpg×ln(\frac{Tsup}{Tsat})=s_{g_{30℃}}+Cpg×ln(\frac{Tsup}{Tsa}t)$

$5.5789+2.8×ln⁡(\frac{16+273}{-10+273})=4.9842+2.8×ln⁡(\frac{T2}{30+273})$

T2=411.74 K=138.74 °C

$h1=h_{g_{-10℃}}+Cpg(Tsup-Tsat)$

=1426.6+2.8(16-(-10))

h1=1499.4 kJ/kg

$h3=h_{f_{30℃}}=323.1 kJ/kg$

h3=h4=323.1 kJ/kg

$h2=h_{g_{30℃}}+Cpg(Tsup-Tsat)$

=1468.9+2.8(138.74-30)

=1773.372 $\frac{kJ}{kg}$

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

COP=4.294

Also, $Q ̇_a=m ̇_R×(h1-h4)$

mass flow rate,$m ̇_R=0.02975 \frac{kg}{sec}$

Volume of refrigerant handled by compressor, V1

$v1=v_{g_{-10℃}}$×$\frac{Tsup}{Tsat}=0.4189$×$\frac{289}{263}$=$0.4603 \frac{m3}{kg}$

$V1= m ̇_R×v1=0.01369 \frac{m3}{s}=0.8216 \frac{m3}{min}$

Temperature of refrigerant at compressor delivery = T2=$138.74 °C$