A well-insulated cylindrical tank of water with D = 3 m diameter is filled to a
ID: 2995635 • Letter: A
Question
A well-insulated cylindrical tank of water with D = 3 m diameter is filled to a depth of H = 6 m. It is
desired to lower the temperature of the water in the tank from T1=20o
C to T2=2
oC in two hours
using a heat pump.
1) Draw a schematic diagram of the the heat pump with all the modes of energy transfer being
clearly identified.
2) Does the atmospheric temperature where the heat is rejected in the heat pump matter to the
performance of the heat pump? Why?
3) If heat is to be rejected to the atmosphere at Tamb=38oC , what is the minimum average
power that must be supplied to achieve this cooling. State all assumptions that you employ.
Explanation / Answer
2)
Yes, it matters. Because it decides entropy generation.
3)
Mass m = density*volume
= 1000*(3.14/4 *3^2 *6)
= 42390 kg
Heat needed Q = m*Cp*(T1 - T2)
= 42390*4.2*(20-2)
= 3204684 kJ
COP of heat pump =
W/Q = (38-20)/(20+273)
W = 3204684* (38-20)/(20+273)
= 196874.8 kJ
Power = 196874.8 / (2*60*60)
= 27.34 kW
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