4) A ground source heat pump heats a building by extracting heat from the ground and pumping it into the building. Define: Qc = heat extracted from the ground, Qn= heat pumped into the building, W = electric energy used by the heat pump, Tc= temperature of the ground, T = temperature of building (Qc, Qn, and W are positive by definition). Assume Tr > Tc. a) Draw a diagram showing energy flow in and out of the heat pump. b) Write a general expression for the change AS in the entropy of the "universe", that is the heat pump plus the cold and hot reservoirs, in terms of the quantities defined above. Now assume ideal (reversible) operation, and take Te= 10 °C and Tp= 20 °C. What is the coefficient of performance (ČOP) of the heat pump? By what factor would this change if we had Tc = 0 °C instead?

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4) A ground source heat pump heats a building by extracting heat from the ground and pumping
it into the building.
Define: Qc = heat extracted from the ground, Qn= heat pumped into the building,
W = electric energy used by the heat pump, Tc= temperature of the ground, T = temperature
of building (Qc, Qn, and W are positive by definition). Assume Tr > Tc.
a)
Draw a diagram showing energy flow in and out of the heat pump.
b)
Write a general expression for the change AS in the entropy of the "universe", that
is the heat pump plus the cold and hot reservoirs, in terms of the quantities defined above.
Now assume ideal (reversible) operation, and take Te= 10 °C and Tp= 20 °C.
What is the coefficient of performance (ČOP) of the heat pump? By what factor would
this change if we had Tc = 0 °C instead?
Transcribed Image Text:4) A ground source heat pump heats a building by extracting heat from the ground and pumping it into the building. Define: Qc = heat extracted from the ground, Qn= heat pumped into the building, W = electric energy used by the heat pump, Tc= temperature of the ground, T = temperature of building (Qc, Qn, and W are positive by definition). Assume Tr > Tc. a) Draw a diagram showing energy flow in and out of the heat pump. b) Write a general expression for the change AS in the entropy of the "universe", that is the heat pump plus the cold and hot reservoirs, in terms of the quantities defined above. Now assume ideal (reversible) operation, and take Te= 10 °C and Tp= 20 °C. What is the coefficient of performance (ČOP) of the heat pump? By what factor would this change if we had Tc = 0 °C instead?
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