A heat pump is used to keep a house warm at 22C. Part A: How much work is requir
ID: 1467059 • Letter: A
Question
A heat pump is used to keep a house warm at 22C. Part A: How much work is required of the pump to deliver 3500 J of heat into the house if the outdoor temperature is 0C. Assume a COP of 3.0. Part B:How much work is required of the pump to deliver 3500 J of heat into the house if the outdoor temperature is -15C? Assume a COP of 3.0. Part C: How much work is required of the pump to deliver 3500 J of heat into the house if the outdoor temperature is 0C. Assume an ideal (Carnot) coefficient of performanceCOP = TH/(THTL). Part D: How much work is required of the pump to deliver 3500 J of heat into the house if the outdoor temperature is -15C. Assume an ideal (Carnot) coefficient of performance COP = TH/(THTL). PLEASE SHOW ALL OF YOUR WORK!
Explanation / Answer
Coefficient of performance (COP) =Q/W where Q=the heat supplied to house, W=workdone by heat pump
part (A). Q=3500J ; COP = 3.0 ;
hence W= 3500/3.0 = 1167 J
part (B). Q =3500J ; COP =3.0;
hence W=3500/3.0= 1167 J
part (C). Q= 3500J ; COP=TH/(TH-TL) = Q/W
TH = 273.15+22=295.15 K ; TL= 273.15+0= 273.15 ; TH-TL = 22 K;
COP=295.15/22 = 13.4
Q/W=13.4
W=3500/13.4 = 261 J
part (D). Q=3500J ; COP=TH/(TH-TL) = Q/W
TH = 273.15+22=295.15 K ; TL= 273.15-15= 258.15 ; TH-TL =37 K;
COP = 295.15/37 = 8.0
W=3500/8 = 438 J