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College Physics | 1st Edition | ISBN: 9781938168000 | Authors: Paul Peter Urone, Roger Hinrichs
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(a) What is the best coefficient of performance for a heat

Chapter 15, Problem 41

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QUESTION:

Problem 41PE

(a) What is the best coefficient of performance for a heat pump that has a hot reservoir temperature of 50.0ºC and a cold reservoir temperature of −20.0ºC ? (b) How much heat transfer occurs into the warm environment if 3.60×107 J of work ( 10.0kW ⋅ h ) is put into it? (c) If the cost of this work input is 10.0 cents/kW ⋅ h , how does its cost compare with the direct heat transfer achieved by burning natural gas at a cost of 85.0 cents per therm. (A therm is a common unit of energy for natural gas and equals 1.055×108 J .)

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QUESTION:

Problem 41PE

(a) What is the best coefficient of performance for a heat pump that has a hot reservoir temperature of 50.0ºC and a cold reservoir temperature of −20.0ºC ? (b) How much heat transfer occurs into the warm environment if 3.60×107 J of work ( 10.0kW ⋅ h ) is put into it? (c) If the cost of this work input is 10.0 cents/kW ⋅ h , how does its cost compare with the direct heat transfer achieved by burning natural gas at a cost of 85.0 cents per therm. (A therm is a common unit of energy for natural gas and equals 1.055×108 J .)

ANSWER:

 Solution  41PE

a)

COPhp  =    Th / Th - Tc

COPhp = (50 OC +273.15 ) K  / (50 OC +273.1

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