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So I was thinking about air conditioner today and how we run air across compressed freon to cool down air but why do we need freon at all why not store just compressed air. My guess is because its inefficient.

My question given a 1 cubic meter tank of air, if the room temperature at 1 atmosphere is 80 degrees. At what atmosphere would you have to have the tank so that the initial release of the air would be the temperature 70 degrees?

Let's first walk you through the usual refrigeration cycle:

1. We compress the freon, which heats it up. That's because we've put energy into in during the compression: It took work to push the piston.




2. Next we cool the gas back to room temperature. That's the big black coil on the back of the fridge.




3. Then we let it expand. The expansion cools the gas, because it does work (energy is removed) as it expands. Since it started at room temperature, it's cooler than room temperature after the expansion.




4. Finally, we let that cool gas absorb heat energy from whatever we want to keep cold. That warms the gas a bit, and gets us ready to start the cycle again.

If we didn't have step 2, the expansion in step 3 would just be the reverse of step 1 and get the freon back where it started. But since we did some of the cooling in step 2 (which we can do because it's hot from the compression), we end up with colder-than-room-temperature gas after 3.

Now, why do we do this with freon? The process I described above is for something like air which stays gaseous throughout. If you use freon (or sometimes ammonia or other chemicals) that will switch between gas and liquid during the process, it becomes more efficient. The physics is still basically the same, it's just that the boiling and condensing can transfer more heat energy without having to use really high pressures.

Back to a gas like air: If you want to calculate how much it chills as it expands, you're talking about "adiabatic expansion". The Wikipedia article is a good starting point. For that operation, there's a relation between the initial and final pressure and temperature:

$$P_i^1-gammaT_i^gamma = P_f^1-gammaT_f^gamma$$

Where $gamma = 1.6$ is a constant value for air. If we take the initial temperature to be roughly 80F or 300K, the final temp to be 70F or 295K and the final pressure to be $P_A = 10^5$ for atmospheric, then

$$ P_i = P_f (T_f/T_i)^gamma/(1-gamma) $$

$$ P_i = (10^5) (295/300)^1.6/(-0.6) = 106,000$$

That's a messy calculation, but because of the exponents ends up being that about a 6% increase in the pressure, when let out, will given you a 10F decrease in the temperature. In US units, that's from 14.7 PSIA to 15.6 PSAI; not all that much. Of course, a 10F drop isn't really enough to run a refrigerator that you'd really want...

Compression brings the molecules closer together thus cooling it down.

This isn't correct. The temperature of a gas isn't related to how close together the molecules are, but their speed.

By compressing the gas, they are closer together, but the work done in compression has sped them up as well. If you wait a while and let the gas cool, they'll still be closer together, but will be moving at the original speed.

My question is given air pressure at sea level. 80 degrees at 14.70 psi, how much pressure would you have to add to cool the air to 70 degrees if it was stored in a tank for 1 cubic meter?

There is no such pressure. Applying pressure will increase the temperature in the short term, not lower it. Any temperature change by doing this is only temporary. The gas will then exchange heat with the environment and move to ambient temperature.

I will address the use of air rather than freon (or its current replacement) as a refrigerant. I believe @BowlOfRed has satisfactorily answered your other questions.

Air is not used as a refrigerant because it would not be practical. This is because a refrigerator requires the use of a working fluid that can undergo phase changes (gas to liquid in condenser, liquid to gas in evaporator) at practical operating pressures and temperatures. Air cannot undergo phase changes except at extremely low temperatures.

For example, at 1 atmosphere the boiling/condensing point of refrigerant HFC-134a (which has replaced freon for environmental reasons) is about -25 C (-13 F). This is somewhat lower than the setting of a household freezer. In contrast, the boiling/condensing point of liquid air at 1 atmosphere is -194.4 C. In order to increase the boiling/condensing temperature to that required by the refrigerator, extremely impractically high pressure would be required.

Hope this helps.