Using heat pump to make a house heater

In summary: Since the efficiency is less than one, the power supply must be higher than the useful power output. In summary, the theoretical minimum power that the heat pump must be supplied in order to provide 4000 watts of heating power is approximately 243.9 watts. This is due to the fact that the efficiency of the heat pump is less than one, making the power supply higher than the useful power output.
  • #1
Pouyan
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A heat pump in winter heat energy from the bottom of a lake, where temperature is 4 ° C and delivers thermal energy in a home where the temperature is 22 C. What is the theoretical minimum power the heat pump must be supplied to you at home must be able to take out 4000 watts heating power ?! Relevant equations
What I learned is this :

for heat pump:
When we will use heat pump to make a place heater:
(ΔQ/ΔW) ≤ T(hot) / T(hot) - T(cold)

And η = (Useful energy/Supply energy)
The attempt at a solution
I see in my solution that the answer is near 244 W
My attempt is :

η=T(hot) / T(hot) - T(cold) = 295 / 22-4 ≈ 16.4

η = P useful/ P Supply

P useful = 4000W and η= 16.4 then P supply = 243.9 W

But is this right ?! Can "η" be more than 1 ?! If the answer is positive is this because of heat pump which is inverse of heat engine and actually is a reversible process ?!
 
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  • #2
##{T_{hot}}## will always be greater than ##{T_{hot}-T_{cold}}##.

Therefore the ratio ##\displaystyle \frac{T_{hot}}{T_{hot}-T_{cold}}## will always be greater than one.
 
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  • #3
Pouyan said:
If the answer is positive is this because of heat pump which is inverse of heat engine and actually is a reversible process ?!

The heat pump is the reverse of the heat engine, but anyone specific heat pump cannot be reversed and turned into a heat engine unless it's a reversible engine.

Note that the efficiency of an engine is always less than one, even in the case of the reversible engine.
 
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FAQ: Using heat pump to make a house heater

What is a heat pump?

A heat pump is a heating and cooling system that transfers heat from one location to another using electricity. It can be used to both heat and cool a house, making it an efficient and versatile choice for home heating.

How does a heat pump work?

A heat pump works by extracting heat from the air, ground, or water and transferring it into a space to heat it. It uses a refrigerant to absorb and release heat as it circulates through the system, similar to how a refrigerator works.

What are the benefits of using a heat pump for house heating?

There are several benefits to using a heat pump for house heating. It is energy efficient, as it only uses electricity to transfer heat rather than creating it. It can also be used for both heating and cooling, making it a versatile option. Additionally, it is environmentally friendly, as it does not rely on fossil fuels.

What are the different types of heat pumps?

There are three main types of heat pumps: air source, ground source, and water source. Air source heat pumps extract heat from the outside air, ground source heat pumps use the constant temperature of the ground to transfer heat, and water source heat pumps extract heat from a water source such as a lake or well.

What factors should be considered when choosing a heat pump for house heating?

When choosing a heat pump for house heating, it is important to consider the climate, size and layout of the house, and the type of heat pump that is most suitable for the location. It is also important to consider the energy efficiency, cost, and maintenance requirements of the heat pump.

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