I have this question / problem in my mind for an estimated of ~20 years. Obviously, my life does not depend on the solution, but the quality of the life of my brain might get improved :)
Shortly: How is a refrigerator / freezer / air conditioner designed, in order to satisfy the needs where they will be used? Or with other words: How are they designed in order to be capable to transfer the required amount of energy (heat) in the desired direction?
I guess that the main input information is:
- the amount of energy needed to be transferred per unit of time;
- the desired range on temperatures on one side;
- the available range of temperatures on the other side.
The desired output parameters:
- the lengths and diameters of the pipes used for the radiators;
- the surfaces of the fins of the radiator;
- the power of the compressor;
- the working fluid, ventilators... are less of a concern at this stage of the problem solving.
I searched on the internet many times about this, but I never really found anything helpful enough.
Note: I already understand quite well how heat pumps work. Just a picture with a bubble as a compressor, and with a thick line, half red, half blue going out and back into the compressor, is very far from my expectations.
I was passionate a long time ago about having a performant computer, and therefore cooling was an important issue. Studying air cooling water cooling, off-the-shelf product, DIY solutions... I ended up with the idea to just put the computer in the fridge / freezer. I quickly understood that a basic fridge / freezer will not do the job - considering that they need up to 24 hours to reach the final temperature from room temperature, with no additional heat added.
At the time of the "problem creation", I had in mind a generic ATX power supply of 400W. Taken to the extreme (and overly simplified), the computer using that power supply generated maximum 400W of heat per unit of time, which the fridge needed to evacuate - just to keep the temperature constant. To actually cool, the capability of the fridge needed to be increased beyond the 400W transferred per unit of time.
Currently I use laptops, so the original problem kind of went away. At least for the time being.
My current understanding
I think that the basis of the calculations starts with the formulas:
pV = nRT (1)
and as a consequence:
p1 V1 / T1 = p2 V2 / T2 (2)
However, these formulas hold true when the chamber is fully enclosed / sealed, and there is no exchange of molecules with the outside world. But in the heat pump, there are 2 volumes, which (almost) permanently exchange molecules.
So another formula is:
V1 + V2 = constant (3)
Of course, I ignored the volume of fluid trapped in the compressor.
Another thing to take into consideration is that the fluid changes its phase from gas to liquid and from liquid to gas.
So how do formulas (1) and (2) change taking the reality into consideration? I might be able to calculate the system "if the cows are spherical and in perfect void", but with real cows living in Earth's atmosphere, things get more complicated.
I will not really design or build any heat pump any time soon, but having a good, real-life understanding of it, will bring me a lot of peace of mind.
I do not need all the deep, complicated mathematics (I might not even understand it properly), but I reject no information either. Also, I do not plan to get a university degree just to understand the physics behind this issue.
Note: The only related question I found on the site about heat pumps is this one. While it touches a very important detail, it is still far from what I ask for.