Question

QUESTION 4 (a) Derive and expression for the coefficient of performance (COP) of a completely reversible heat pump in terms of the thermal energy reservoir, high temperatures T, and low temperature 1, respectively. Draw a diagram that support the COP derivation. [7 marks] (b) A Heat Pump (HP) is to be used for heating a bouse in winter as illustrated in Figure Q4(b). The house is to be maintained at 26°C at all times. When the temperature outdoors drop to -4°C, the beat losses from the house are estimated to be 55000 kJ/h. Determine the minimum power in kW required to run this heat pump if heat is extracted based on the following conditions: (i) The outdoor temperature is at -4°C. [3 marks] (ii) The well water temperature at 10°C. [5 marks] House Indoor House Outdoor Figure Q4(b): Heat pump

termo

Answer 1

(a) Hugh termperatuses 4 Qovr- Compressov Turbine Conden ser Eaporatov TL Low Temperatune Consider Ahe reverside TH healr pump Cycle on T-S diagram stown in Jrqure. COP wner i we-wir = Qaur -in wner Ctrst law heimadynenmics} a- 1- 2 - 3-4-6 Gvea Gvea a - !-4-6-a Wner! wi = (avea a-1- 2-3-4-b)-Careaa a-1- 4-b-a ) Grea ! - 2 -3-4-1

a - \ - 2-3-4-ం Ce COP ు Cఒట 1-2 -2-4- 1 T ఏ - ) (TH-TL) ( Sa-Sb) TH TH- TL క 000 b ci) TH = 26 c - 244 K TH=299K ఓ = 269 k 0c Tu = -4 ఉ: ఇరింద K|h ఈ ఏcco3రర ఓ,28Kw TL=269K COP 299 ా 9.97 TH-TL 299- 269 ఉ COP Powed 15.28 K = li53 kW 9,97 - :

TH = 26°c - gqak Te= 10°c = 283に %3D 15.28 K TH 299 = 18.7 TH-Te 299-283 Power i - 15.28KW Ans 0,82 KW %3D 18.7