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A vapour compression system using R12 works between -$150^0$ C and $350*0$ 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 = 80% iv) Heat rejected in the condenser per TR.

Marks: 5M, 6M

Year: Dec2014, Dec2015, Dec2013, May2014

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$T_E=T_{sat_{Pe}}=-15℃,T_C=T_{sat_{Pc}}=35℃$

From P-H chart of R-12,

We know that at point 1,

$h_1=181 \frac{kj}{kg};h_2=210 \frac{kJ}{kg};h_3=h_4=68 \frac{kJ}{kg}$

$COP=\frac{R.E}{Wc}=\frac{181-68}{(210-181}=3.896$

Also,

$Q_a=m ̇_r×(h_1-h_4 )$

For 1 TR capacity,

$1×3.5=m ̇_r (181-68)$

$m ̇_r=0.0309 \frac{kg}{sec}=1.8584 kg/min$

Also

$m ̇_r×v_1=piston \ displacement \ per \ TR ×η_vol$

$v_1=0.076 m^3⁄kg \ from \ p-h \ chart$

Therefore,

piston displacement per $TR=0.1765 m^3⁄min$

Rate at which heat is rejected in condenser per TR

$Q_r=m_R×(h_2-h_3 )$

$=0.0309×(210-181)$

$=0.899\frac{ kJ}{sec}$

We know, ideal COP

$=\frac{T_E}{T_C-T_E}$

$=\frac{258}{308-258}$

=5.16