4 A heat pump uses R134a as the refrigerant and operates on

4. A heat pump uses R134a as the refrigerant and operates on an ideal vapor compression heat pump cycle. The heat rate to a building is 15 kW in order to maintain the interior temperature at 20 °C when the outside is 5 °C. Saturated vapor at 2.4 bar leaves the evaporator, and saturated liquid at 8 bar leaves the condenser. Find (a) the compressor power in kW (5 points), (b) the COP, (5 points) and the COP for a reversible Carnot heat pump operating between the thermal reservoirs (5 points).

Solution

From R-134a properties at P1 = 2.4 bar and quality = 1 (sat. vapor) we get, h1 = 247 kJ/kg, s1 = 0.935 kJ/kg-K

From R-134a properties at P2 = 8 bar and s2 = s1 = 0.935 kJ/kg-K we get T2 = 36.1 deg C, h2 = 272 kJ/kg

From R-134a properties at P3 = 8 bar and quality x3 = 0 (sat.liq) we get h3 = 95.5 kJ/kg

a)

Heat rate to the building = m*(h2 - h3)

= m*(272-95.5)

= m*176.5 = 15

m = 0.085 kg/s

Compressor power = m*(h2 - h1)

= 0.085*(272-247)

= 2.125 kW

b)

COP = Heat supplied / Power input

= 15 / 2.125

= 7.06

c)

Ideal COP = T_high / (T_high - T_low)

= (20+273) / (20-5)

= 19.53