Calculating Heat Expelled from a Heat Pump

In summary, the heat pump has a coefficient of performance of 7.05 and absorbs 20 cal of heat from the cold outdoors in each cycle. To find the heat expelled to the warm indoors, we use the equation Qh/W = 7.05 where Qh is the heat expelled to the warm indoors and W is the work done in one cycle. With this equation, we can calculate that Qh is 23.306 cal/cycle. Energy is conserved in this process, but it takes work (possibly from electricity) to operate the pump. The fraction of heat obtained for free from the outside is approximately 3.306/23.306, or 1/7th of the total heat output.
  • #1
jdog6
17
0
A heat pump has a coefficient of performance of 7.05. If the heat pump absorbs 20 cal of heat from the cold outdoors in each cycle, find the heat expelled to the warm indoors. Answer in units of cal.
I believe COP (heating mode) : 7.05 and COP = Qh/W
Qc = 20 cal
so I have to find Qh= ? cal
I don't know an equation to put all this together?
Please help, thank you.
 
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  • #2
Is Energy conserved?

If the coeff. of performance is 7.05,
how much Work is done in one cycle?
 
  • #3
the question does not say all i have is what i posted
 
  • #4
The entire subject of Thermodynamics
is FOUNDED on Conservation of Energy
(Energy can be moved around, but not created/destroyed).

So, YES, Energy is conserved.

Where do you think the Energy comes from,
that is dumped into the (warm) room?
 
  • #5
The energy comes from rods outside.
 
  • #6
Not all of it ... it takes *Work* to operate the pump!
Qh/W = 7.05 , so you have to PAY for the Energy
(electricity, probably) for the W = Qh/7 of the heat.

So, what fraction do you get "for free", from outside?
 
  • #7
Qh=W+Qc so W=(W+20)/7.05
7.05W-W=20
W(7.05-1)=20
6.05W=20
W=20/6.05
W=3.306
Qh=3.306+20
Qh=23.306 cal/cycle
and to check it 23.306/3.306=7.05
 

1. How do you calculate the heat expelled from a heat pump?

To calculate the heat expelled from a heat pump, you will need to know the COP (Coefficient of Performance) of the heat pump, the amount of electricity used by the heat pump, and the ambient temperature. The formula for calculating heat expelled is: Heat Expelled = COP x Electricity Used x (1 - Ambient Temperature/Indoor Temperature)

2. What is the COP of a heat pump?

The COP (Coefficient of Performance) of a heat pump is a measure of its efficiency. It is the ratio of the amount of heat output to the amount of electricity input. The higher the COP, the more efficient the heat pump is at transferring heat.

3. How does ambient temperature affect the heat expelled by a heat pump?

Ambient temperature plays a crucial role in the amount of heat expelled by a heat pump. As the outdoor temperature decreases, the heat pump has to work harder to extract heat from the outside air. This results in a lower COP and less heat expelled. On the other hand, in warmer temperatures, the heat pump has an easier time extracting heat, resulting in a higher COP and more heat expelled.

4. Can the heat expelled by a heat pump be used for both heating and cooling?

Yes, heat pumps can be used for both heating and cooling. In the winter, they extract heat from the outside air and transfer it inside to heat a space. In the summer, they extract heat from the inside and transfer it outside to cool a space. This is why heat pumps are often referred to as "reversible" systems.

5. Are there any factors that can affect the accuracy of heat expelled calculations?

Yes, there are several factors that can affect the accuracy of heat expelled calculations. These include the age and condition of the heat pump, the quality of the installation, and the type of heat pump (air-source or ground-source). Additionally, other factors such as climate, insulation, and the size of the space being heated or cooled can also impact the accuracy of calculations.

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