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1. Sep 30, 2014

### Jake Drinkwater

Hi, this is my first post on here. My question relates to adiabatic cooling/heating of a gas. I am trying to grasp the idea conceptually rather than being able to explain it mathematically per se....

When gas escapes rapidly from a pressurised cylinder the rapid expansion of the gas is facilitated by the heat energy within the gas, causing its temperature to fall (as there has been no time for the transfer of heat energy from the surrounding environment).

However, the First Gas Law states; P1/V1 = P2/V2 @ constant temperature.

There has been in increase in the volume of the gas but there has also been a reduction in the pressure of the gas. Would not the potential energy of the high pressure of the gas (when in the cylinder) be enough to account for the increased volume of the gas at greater volume (once escaped from the cylinder)?

Or, if you were to look at it in terms of the ideal gas equation; PV = nRT, I would expect that as the volume increased, the pressure would decrease in accordance with this and the temperature would remain constant.

I don't understand why the 'system' needs the addition of energy (taken from the heat energy of the gas in the case of an adiabatic process).

2. Sep 30, 2014

### Matterwave

I don't think I understand your question, perhaps you can rephrase more clearly exactly what you're asking? An ideal gas which undergoes adiabatic free-expansion remains at constant temperature, this is because the temperature is only dependent on the energy of the system, and since in a free-expansion there is no work being done and adiabatic means no heat is exchanged, the Energy of the gas, and therefore the temperature of the gas, will remain constant (for an ideal gas).

Also, the Ideal gas law states P1V1=P2V2 @ constant temperature (and particle number), I don't know what you mean with "first gas law", but it is not the ratio P/V which remains constant at constant temperature (and particle number), but the product PV.

3. Sep 30, 2014

### Staff: Mentor

The gas that remains in the cylinder does work on the gas that it forces out of the cylinder so that, under adiabatic conditions, its internal energy decreases. This means that its temperature decreases.

Chet