A $10°C$ and $35°C$ 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 = 84%

iv. Heat rejected in the condenser per TR

v. Ideal COP

Marks: 12M,

Year: Dec2014, Dec2015, Dec2013, May2014

Difficulty: Medium

$T_E=T_{sat_{Pe}}=-10℃,T_C=T_{sat_{Pc}}=35℃$

From P-H chart of R12,

h1=348 kJ/kg,

h2=371 kJ/kg,

h3=h4=234 kJ/kg

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

COP=4.9565

Also, $Q ̇_a=m ̇_R×(h1-h4)$

For 1 TR capacity, $1 x 3.5= m ̇_R×(348-234)$

mass flow rate,$m ̇_R=0.031 \frac{kg}{sec}=1.842 \frac{kg}{min}$

Also, $m ̇_R×v1=piston \ displacement \ per \ TR×η_{vol}$

v1=0.076 m3/kg from p-h chart

Therefore, piston displacement per TR = 0.1667 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