A heat pump working on the Carnot cycle takes in heat from a reservoir at 5 °C and delivers heat to a
reservoir at 60 °C. The heat pump is driven by a reversible heat engine which takes in heat from a reservoir at
840 °C and rejects heat to a reservoir at 60 °C. The reversible heat engine also drives a machine that absorbs
30KW. If the heat pump extracts 17 KJ/s from the 5 °C reservoir, determine (a) the rate of heat supply from the
840 °C source, and (b) the rate of heat rejection to the 60 °C sink
Answers
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Answer:
a. the rate of heat supply from the
840 °C source =Q1=??
b. the rate of heat rejection to the 60 °C sink =Q2 +Q3 =??
A.
Efficiency of the heat engine
η=1 - T2/T1
=1-333/1113
=0.7
Also, η=(Q1 - Q2) /Q1
So ( Q1 - Q2) =ηQ1
The C.O.P of heat pump
( COP) =T2 /(T2 - T3)
=333/(333-278)
=6.05
Also the C.O.P of the heat pump is
COP = (Heat supplied) / (work supplied )
=Q4/Wp
6.05 = 17 /Wp
Wp=2.81 kW
Total work
W=We - Wp
30kW =We - 2.81
We =32.81kW
But We = Q1 - Q2
=ηQ1
32.81= 0.7 Q1
Q1 =46.87 kW
B. We = Q1 - Q2
Q2 =46.87 -32. 81
=14.06 kW
Q3 =Q4 + Wp
=17+2.81
=19.81
Q2 +Q3 =33.87 kW