# How to design a fridge / freezer / air conditioner / heat pump?

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.

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.

History

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.

Bottom line

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.

• Instead of searching the internet,. find a site selling books and look for something like "Engineering Thermodynamics, Work and Heat Transfer" by Rogers and Mayhew. Theory is all there and there are many similar books... Commented Dec 2, 2021 at 20:23
• If the device generates 400W of heat and you remove 400W of heat, you do not need additional cooling. Additional cooling would freeze the cow! You wish to maintain equilibrium. Commented Dec 2, 2021 at 20:34
• @StainlessSteelRat: If I would design and build such a machine, the thing would be thermo-regulated with some sensors etc. E.g., looking at the temperature of the processor, or the temperature of the air at the "out side" of some ventilator. To maintain equilibrium is of course the target, but there are as many eq. points as there are temperatures in a continuous analogic range :) First, basic design. Then, going to the details. And the extra cooling might be needed if the cow arrives in liquid form and has to be stabilized quickly - assuming it will not be damaged by the thermal shock :) Commented Dec 2, 2021 at 20:44
• The conversion process is not perfect and there are losses, say 450W required. 3600W is 1 RT (Refrigerated Ton of cooling). You need 0.125 RT of cooling. Commented Dec 2, 2021 at 20:57
• @Fred: that site looks fishy at best. It redirects to a different site every time when I click "Download", I have to create at least 2 accounts on 2 different sites, and I have to provide full credit card info. I will not do that. I am curious if anyone else succeeded to use the above-mentioned site successfully. Commented Dec 3, 2021 at 17:22

### You need much more than PV=nRT

The key feature of a refrigeration system is using the heat of vaporization/fusion to move heat.

What you need:

• Thermodynamics
• Fluid dynamics
• Heat Transfer
• Circuits

Designing a refrigeration/heat pump system from scratch would be a stretch for any Mechanical Engineering BS graduate. There is a lot going on there. A specific refrigeration component design book would be required, but would need the above skill sets to understand.

If what you want is to understand how these processes work, then Wikipedia is enough to get started if you're willing to search out info on every topic you don't understand.

• As I mentioned, I already know the overly simplified principle presented on Wikipedia - the compressor with the red line ans the blue line... Commented Dec 3, 2021 at 17:25
• I'm not trying to be a jerk, but you wouldn't use PV=nRT as the governing principle if you understood the principles involved. The capacity of a refrig. system are governed by mass flow rates, choice of refrigerant, and heat transfer from the evap/condenser. Commented Dec 3, 2021 at 17:53
• I do not consider you a jerk, do not worry. I did not claim that I know much, and I surely did not claim that the pV=nRT is the governing principle. I only thought that a starting point in thinking the things would be this formula - but modified because of the "flow" (fluid being exchanged between the cold and warm "halves"). I have no idea about how the formula would change for this situation. I imagine that the formula still holds true for infinitesimal volumes (when they travel along the tubes, and especially when they switch "sides"), and then some integral calculations would "happen". Commented Dec 3, 2021 at 18:00
• the starting point is how much mass per time changes state in the evaporator and condenser. Commented Dec 3, 2021 at 19:36
• In my mind, the working fluid was always a gas (possible, but not "optimized"). However, you reminded me that I read on the net (in the more-or-less distant past) that the change of state (gas-liquid) is more than welcome. Commented Dec 7, 2021 at 21:36