A heat pump in a home is to serve as a heater in winter and an air conditioner i
ID: 1940264 • Letter: A
Question
A heat pump in a home is to serve as a heater in winter and an air conditioner in summer. This device transfers heat from its working fluid to air inside the house during the winter and to air outside the house during the summer. The design conditions (worst case) are as follows.
Winter
inside house=70.0 degrees F
outside house=20.0 degrees F
Q(dot)=-50.0E3 Btu/h
Summer
inside house=70.0 degrees F
outside house=100. degrees F
Q(dot)=30.0E3 Btu/h
Use the reversible Carnot cycle to determine the minimum power required to drive the heat pump.
Explanation / Answer
in winter efficiency=1-(20/70)=5/7 Q(dot) means heat loss per time=50.0*10^3 *1 055.05 J/h (1btu= 1 055.05J) 5/7=(heat input-heat loss)/heat input =>heat input=heat loss *7/2=50.0*10^3 *1 055.05*7/2=1.84*10^8 J/h in summer similarly, efficiency=1-(7/10)=3/7 Q(dot) means heat loss per time=30.0*10^3 *1 055.05 J/h (1btu= 1 055.05J) 5/7=(heat input-heat loss)/heat input =>heat input=heat loss *7/2=(30.0*10^3 *1 055.05) *10/7=4.52*10^7 J/h