- #1
bkraabel
- 26
- 0
Homework Statement
In winter, you like to keep your house interior at 21.0 degrees C. Your geothermal
heating system, which was advertised as being reversible, draws thermal energy from an
underground reservoir at 347 K. In a cold winter, with the average outdoor temperature
being 0.0 degrees C, thermal energy escapes from the house at a rate of 1000 W +-5 percent.
Distributing the thermal energy supplied by the heating system throughout the house
requires 180 W (provided by the heating system). Is your heating system reversible
within your 5% margin of error, or was the advertisement false? Ignore any inefficiency
in converting electrical energy to mechanical energy
Homework Equations
For reversible heat pump, coefficient of performance is the maximum possible:
[itex]COP_{max} =\frac{T_{out}}{T_{out}-T_{in}}[/itex]
where [itex]T_{in}=273[/itex] K and [itex]T_{out}=294[/itex] K (I think).
For reversible heat engine (Carnot engine), maximum efficiency is
[itex]\eta_{max} =1-\frac{T_{out}}{T_{in}}[/itex]
where [itex]T_{in}=347[/itex] K and [itex]T_{out}=294[/itex] K (I think).
The Attempt at a Solution
I don't see how to relate these efficiencies (or anything else) to the power requirements of 1180 W. Also, I don't see how the outdoor temperature of 0 Celsius is relevant; it seems like we're just transferring heat from the ground to the house.
Last edited: