TITLE.PM5

758 ENGINEERING THERMODYNAMICS

dharm

\M-therm\Th14-3.pm5

p

h

4 3

1 2

Condensation 3 ′

Evaporation

Throttling

Compression

Heat extracted per kg of refrigerant

= 187.53 – 69.55 = 117.98 kJ/kg

Refrigerant flow rate =^325

117 98.

= 2.755 kg/s

Compressor power = 50 kW

∴ Heat input per kg =

50

2.755 = 18.15 kJ/kg

Enthalpy of vapour after compression

= h 2 + 18.15 = 187.53 + 18.15

= 205.68 kJ/kg

Superheat = 205.68 – h 3 ′ = 205.68 – 201.45

= 4.23 kJ/kg

But 4.23 = 1 × cp (t 3 – t 3 ′) = 1 × 0.6155 × (t 3 – 35)

∴ t 3 =

423

06155

.
.

• 35 = 41.87°C. (Ans.)
  Note. The compressor rating of 50 kW is assumed to be the enthalpy of compression, in the absence of any
  data on the efficiency of compressor.
  Example 14.24. A vapour compression heat pump is driven by a power cycle having a
  thermal efficiency of 25%. For the heat pump, refrigerant-12 is compressed from saturated vapor
  at 2.0 bar to the condenser pressure of 12 bar. The isentropic efficiency of the compressor is 80%.
  Saturated liquid enters the expansion valve at 12 bar. For the power cycle 80% of the heat
  rejected by it is transferred to the heated space which has a total heating requirement of 500 kJ/min.
  Determine the power input to the heat pump compressor. The following data for refrigerant-12
  may be used :

Pressure, bar Temperature, Enthalpy, kJ/kg Entropy, kJ/kg K

°C Liquid Vapour Liquid Vapour

2.0 – 12.53 24.57 182.07 0.0992 0.7035

12.0 49.31 84.21 206.24 0.3015 0.6799

Vapour specific heat at constant pressure = 0.7 kJ/kg K. (U.P.S.C. 1995)

Solution. Heat rejected by the cycle =

500

8. = 625 kJ/min.
   Assuming isentropic compression of refrigerant, we have
   Entropy of dry saturated vapour at 2 bar
   = Entropy of superheated vapour at 12 bar

0.7035 = 0.6799 + cp ln

T

(.+ )49 31 273 = 0.6799 + 0.7 × ln

T

322 31.

F

HG

I

KJ

or ln

T

322.31

F

HG

I

KJ =

0 7035 0 6799

07

..

.

−

= 0.03371

or T = 322.31 (e)0.03371 = 333.4 K
∴ Enthalpy of superheated vapour at 12 bar
= 206.24 + 0.7(333.4 – 322.31) = 214 kJ/kg
Heat rejected per cycle = 214 – 84.21 = 129.88 kJ/kg

Mass flow rate of refrigerant =

625

129 88. = 4.812 kg/min

Fig. 14.34