(b) The Joule experiment
When there are no interactions between the molecules, the internal energy is independent
of their separation and hence independent of the volume of the sample
(Section 2.2a). Therefore, for a perfect gas we can write πT = 0. The statement πT = 0
(that is, the internal energy is independent of the volume occupied by the sample)
can be taken to be the definition of a perfect gas, for later we shall see that it implies
the equation of state pV ∝ T. If the attractive forces between the particles dominate
the repulsive forces, then the internal energy increases (dU > 0) as the volume of the
sample increases (dV > 0) and the molecules attract each other less strongly; in this
case a plot of internal energy against volume slopes upwards and πT > 0 (Fig. 2.24).
James Joule thought that he could measure πT by observing the change in temperature
of a gas when it is allowed to expand into a vacuum. He used two metal vessels
immersed in a water bath (Fig. 2.25). One was filled with air at about 22 atm and the