# Can a volume of gas be measured by change in PSI?

I had a visit from an air conditioner repairman who brought with him a tank of refrigerant. He measured the system and determined that the pressure was about 20 psi too low. So he added refrigerant to the system until it was right.

When it came time to pay him, he said, "well I had to raise your system by 20 psi so it's going to be [20 x price for 1 psi]."

The price was fine, but I am still wondering: would it have taken the same amount of gas to raise my system from 0 to 20 psi as it would to go from 80 to 100, say?

Or, in other words, is it absurd to charge by pressure delta instead of some more reliable measure of what was dispensed from the tank?

Volume is inversely proportional to pressure only when:

1) the number of moles of gas is held constant. We can say this is true in your situation because the repairman measured the pressure in the tank and I don’t think a significant amount of gas disappeared from the tank in the time it took for him to measure the pressure.

2) The temperature is held constant. Again, I don’t think temperature dropped 20 kelvin in the time it took for him to measure the pressure in the tank.

This follows from the ideal gas law equation – a good approximation most of the time:

$PV=nRT$.

So I say your repairman still has his wits about him and isn’t trying to rip anyone off.

• Sure PV = nRT works... but I think the poster's original comment is also valid. A delta pressure as a unit of "refridgerant" seems a bit odd since different units (heat pumps) will have different volumes. He may not have been trying to "rip off" the customer... but unless all heat pumps have the same internal volume (and they don't) a pressure delta is a strange / semi-bogus way to measure things. The flip side is that there probably are a small number of common volumes for commercial heat pumps, but he didn't say "delta pressure for this size"... – Dan S May 15 '14 at 18:29
• Dan, that's a good point. In Dissenter's defense, though, most of the ACs here are of a very predictable size so his experience may have led him to charge by pressure delta as a rough indication of the material he's dispensed. – Isaac Lubow May 16 '14 at 1:19

In fact $PV=nRT$ works better when you deal with gas at high temperature and low pressure. In your case it depends on the pressure of your conditioner and the compressibility factor of your refrigerant. If you know the refrigerant and his compressibility factor you can evaluate it.