# COP in vapor compression refrigeration analysis

## Main Question or Discussion Point

Hi, has anybody worked with heat pumps? I'm recently confused about how the heat pump compressor operates. Does it have a fixed pressure or it actually adjust its pressure automatically to outdoor temperature variation? All my confusion originate from the following problem:

Now we have a heat pump that employs vapor compression refrigeration cycle for cooling. Suppose indoor temperature is 55 F(12.7 C) and outdoor temperature is 95 F(35 C), try to determine the parameters that compressor should be operating so that COP of 6 can be achieved. Then use the determined parameters to calculate COP when outdoor temperature is raised to 105 F and indoor temperature stays the same. For the sake of simplicity, assume saturated fluid in the condenser and saturated vapor in the entrance of compressor.

Any suggestion will be much appreciated. Thanks.

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russ_watters
Mentor
A heat pump compressor is fixed compression ratio, but not fixed pressure. If the temperature outside drops (in heating mode), the pressure in the entire system will drop.....and the COP will drop. Similarly, if the temperature outside rises when in cooling mode, the COP will drop.

thanks for the reply! so in the cooling mode, when the outdoor temperature is raised, the compression ratio stays the same, but the system pressure drops or rises? and can we calculate this pressure drop or rise based on the assumption of saturation liquid and saturation vapor? and from that we calculate the COP in this case? Thanks.
A heat pump compressor is fixed compression ratio, but not fixed pressure. If the temperature outside drops (in heating mode), the pressure in the entire system will drop.....and the COP will drop. Similarly, if the temperature outside rises when in cooling mode, the COP will drop.

russ_watters
Mentor
In air conditioning mode, if the temperature outside rises, the pressure rises.

Well...it depends on what other information you are given and how you are expected to use it. You can probably plot the cycle on a t-s diagram and work from there. Or maybe they just want you to use the carnot efficiency equation? Part of the difficulty in a calculation, though, is the CoP drop is related to the difficulty with dissipating heat at the heat exchanger when the temperature outside rises.

Thank you very much, Russ Watters! you've been very helpful.
Is it appropriate to assume this pressure is a function of temperature, considering it's saturated at the entrance of the condenser, and this pressure is equal to the pressure at the exit of the compressor? then by using the equation
COP = $$\frac{h_1-h_4}{h_2-h_1}$$,
where 1:entrance of compressor
2:exit of compressor
3:entrance of condenser
4:exit of condenser
but it seems that even with the pressure calculated, we still need to know the temperature at point 2 to determin h2. Can I just assume a temperature at point 2?
by the way, I tried to use carnot cycle efficiency for calculation, but this method was denied...

In air conditioning mode, if the temperature outside rises, the pressure rises.

Well...it depends on what other information you are given and how you are expected to use it. You can probably plot the cycle on a t-s diagram and work from there. Or maybe they just want you to use the carnot efficiency equation? Part of the difficulty in a calculation, though, is the CoP drop is related to the difficulty with dissipating heat at the heat exchanger when the temperature outside rises.

What are the typical cop of vapor compression chiller and absorption chiller