Why expansion of a gas implies cooling?

[jk22]

Normally expansion implies colding, but I don't know how to explain this with the equation of perfect gazes : $PV=nRT$
If V increase then the pressure diminishes. Admitting a constant number of molecules, is the number of shocks is inversely proportional to the volume ? But this only implies a constant temperature, not diminishing of it ?

 

[256bits]

As a brief answer, doing work lowers the internal energy of the particles.

 

[Steve4Physics]

Normally expansion implies colding, but I don't know how to explain this with the equation of perfect gazes : $PV=nRT$
If V increase then the pressure diminishes. Admitting a constant number of molecules, is the number of shocks is inversely proportional to the volume ? But this only implies a constant temperature, not diminishing of it ?

It depends what you mean by 'normally'. For cooling, you are referring to what is called an adiabatic expansion. This is where there is negligible heat-transfer between the gas and its surroundings (because the gas is in a non-conducting container and/or the change is too quick for heat-transfer to occur).
$T = \frac {PV} {nR}$
V increases by some factor f, but P decreases by a factor bigger than f. So the temperature decreases.

Look up 'adiabatic expansion' if you want more detail.

Note: If you supply some heat energy during the expansion, then you can have V increasing by factor f and P reducing by the same factor f. This leaves T unchanged. This is called an isothermal expansion.

It is interesting to see *why* cooling happens, at the particle level. Imagine a syringe full of gas. Particles are continually hitting the piston-face and bouncing off with the same speed. You pull the piston outwards a bit. While the piston was moving outwards, particles were bouncing off the moving surface and therefore their rebound speed was reduced. So the average speed of the gas particles has been reduced.