# Temperature change inside pressure chamber

Let's say there is a pressure chamber with some sort of sample / specimen (e.g. protein crystal) in it. Now I apply a certain amount of gas pressure, e.g. 10 or 20 atm. Let's say I use xenon as a gas.

I'm wondering what will happen to the temperature inside my chamber - from the ideal gas law you get a reciprocal relationship between temperature and pressure, so given all other things stay the same (i.e. the chamber volume), what is the temperature change / final temperature as seen by my sample? I'd start at room temperature and go from there .. Obviously, the gas is compressed to start with (and has a certain temperature as well).

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Charles's law is about interdependence of volume and temperature .. i want to work at constant volume and vary the pressure. Since according to the ideal gas law varying P or V is equivalent, I could still use the same principle as in Charles's law though. However I would get that going from 1 atm at 293 K (ambient conditions) to 2 atm would mean cooling the interior of the chamber by 146.5 K in a (possibly) short amount of time, thereby shock frosting my sample .. is that correct? And does it not make a difference that the gas used for pressurization is already compressed? –  user9730 Mar 27 '13 at 17:16

Lets look at the ideal gas law:

$$PV=NkT$$

You seem to assume that when you increase the pressure in a pressure chamber, all other variables in this formula except the temperature stays constant. That is not how a pressure chamber typically works. Sure, you could build a pressure chamber that works like that. Simply seal the chamber and heat it. This will cause temperature and pressure to rise proportionally, while keeping the other variables constant.

In the kind of pressure chamber I think you have in mind, the pressure is typically increased by pumping more air (or other gas) into the chamber, i.e. increasing $N$. The effect on the temperature will depend on how the compressor works. Here you can read about the temperature effects of compressing gas depending on the process.

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thanks for your reply! i'm not sure we talk about the same thing - obv you influence the observable P by increasing N which is equivalent as can be seen from the ideal gas law. As for your link on gas compression, I appreciate that gas heats as you confine it - but I reckon that's different from what I want to do (sorry for not making that clearer), i.e. using already compressed gas to put it inside a pressure chamber to alter the pressure there. I think this has to happen with an associated cooling down as by increasing N (or P) and keeping V constant T has to drop. –  user9730 Mar 28 '13 at 11:28