How does Joule's Law explain gas temperature change?

[Peter G.]

Hi

I was reading about this experiment done by Joule that consists of:

Some gas was kept in container A. Container A and B were interconnected. He allowed the gas from container A to diffuse, hence, occupying the container B as well. The system was well thermally insulated.

When this happens, there is no change in temperature.

I don't understand how can a change in volume and therefore pressure, not yield any change in temperature!

I was thinking in terms of: T = PV / nR

Temperature is directly proportional to both Pressure and Volume so, if one decreases by a factor x, in this case pressure, and the other, in this case volume, therefore, increases by the same factor, x, the temperature remains the same? And, since we are dealing with an ideal gas, the internal energy is constant.

Is that it?

Thanks,
Peter G.

 

[jbsteele]

Yes, that is it. When the pressure and volume of an ideal gas are changed, while the temperature remains constant, the internal energy of the system is conserved. This is known as Joule's Law. It states that when a gas expands or contracts, the change in internal energy is equal to the work done by the gas. Therefore, as long as the temperature remains constant, the internal energy does not change. This means that when pressure and volume change, no heat is exchanged with the surroundings, and thus, no temperature change is observed.