11 0-3 ponts OSCoPhys1 15.5,041 (e) what is the best coefficient of performance

Question

11 0-3 ponts OSCoPhys1 15.5,041 (e) what is the best coefficient of performance for a heat pump that has a hot reservair termperature of 48.0°C and a cokd reservair temperature of 22.0 c7 (b) How much heat in kilocalories would it pump into the warm environment if 3.60 x 10 J of work (10.0 kw-h) is put into it? (c) Assume the cost of this work input is 10Ac.xw-h. Also assume that the cost of direct production of heat by burning natural gas is 89,0áe per therm (a kcal common unit of energy for natural gas), where a therm equals 1.055 x 10 1. Compare the cost of producing the same amount of heat by each method. (cost of heat pump/ cost of natural gas) Additigihgl Materials Reading 12.- points OSCoPhys1 156050 My when 153 x 1o' J of heat enters a cherry ple initialy at 20.00C, ts entropy Incresses by 05 2/K What is its final temperature?

Explanation / Answer

(a) Coefficient of performance = QH/W = TH/(TH - TC)

Herer Temperature should be in Kelvin

= (273.15 + 48)/[273.15+48 - (273.15-22) = 4.59

(b) As QH/W = 4.59 , QH = 4.59*W = 4.59 *3.6*107 = 1.652*108 J

(c) Cost of heat pump (M1) = 10*10(work done in kW.h) = 100 $

Cost of natural gas (M2)= 89*total energy produced/energy unit

= 89*1.652*108/(1.055*108) = 139.36 %

M1/M2 = 100/139.36 = 0.72

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