A heat pump takes work in the form of electricity and turns it into heating or c
ID: 1769783 • Letter: A
Question
A heat pump takes work in the form of electricity and turns it into heating or cooling. The efficiency of a heat pump is judged by the “coefficient of performance (COP),” which is the ratio of useful heating or cooling divided by the amount of work that is used to run the system.
(a) Does the COP depend on whether the system is run in heating or cooling mode? Explain.
(b) Obtain a limit analogous to the Carnot efficiency for the COP for each case, in terms of the temperatures of the hot and cold reservoirs.
(c) On a cold day in Southern Chester County, PA, when you are running your heat pump to heat your heeeouse, is the “hot” reservoir the inside of the house or the outside air? Would it be more or less efficient to couple the system to the water table (which generally stays at 45 degrees Farenheit or so, regardless of the outside temperature)?
Explanation / Answer
a)
In cooling mode, the device acts like an air conditioner and in heating mode, it acts like a heat pump.
For an air conditioner, the thermal energy is transferred from inside the room to the surroundings.
The COP here is = Ql / W = Tc/ Th -Tc
Ql is the heat transferred and W is the amount of work needed to transfer
For a heat pump, the heat is transferred from the colder surroundings to inside the room.
The COP here is = Qh / Th -Tc
Qh is the heat transfered. Th and Tc are the temperatures of the cold hot and cold compartments respectively
b) Considering the above formulae for COPs, they can be seen as inverse of formulae for efficiences, The value hence can be greater than 1. For actual devices, the values of COPs vary between 3 to 6
c) The hot reservoir will be inside your room, as the heat from the outside is going to be transferred to the room which is to be heated. It is more efficient to couple a water table to the pump because it stays at a constant temp so the work done will be constant as the temperature of the cold source is not reducing.