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A vapour compression system using R134A works between

$-10°C$ and $36°C$ as evaporator and condenser temperature respectively. Using p-h chart determine: i. COP

ii. Mass flow of refrigerant per TR

iii. Piston displacement per TR using volumetric efficiency = 83%

iv. Heat rejected in the condenser per TR

v. Ideal COP

Marks: 12M,

Year: Dec2014, Dec2015, Dec2013, May2014

Difficulty: Medium

1 Answer
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$T_E=T_{sat_{Pe}}=-10℃,T_C=T_{sat_{Pc}}=36℃$

From P-H chart of R134A,

h1=393 kJ/kg,

h2=421 kJ/kg,

h3=h4=253 kJ/kg

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

COP=5

Also, $Q ̇_a=m ̇_R×(h1-h4)$

For 1 TR capacity, 1 x 3.5= m ̇_R×(393-253)

mass flow rate,$m ̇_R=0.025 \frac{kg}{sec}=1.5\frac{kg}{min}$

Also, $m ̇_R×v1=piston \ displacement \ per \ TR×η_vol$

$density \ of \ point \ 1=ρ1=10 \frac{kg}{m3} from \ p-h \ chart$

$v1=0.1 \frac{m3}{kg}$

Therefore, piston displacement per TR = 0.1807 m3/min

Rate at which heat is rejected in condenser per $TR=Q ̇_r=m ̇_R×(h2-h3)=4.247 kJ/sec$

We know, ideal COP = $\frac{T_E}{T_C-T_E}$= 5.844

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