The thermodynamic implications of the experiment are as follows. No work was
done in the expansion into a vacuum, so w = 0. No energy entered or left the system
(the gas) as heat because the temperature of the bath did not change, so q = 0.
Consequently, within the accuracy of the experiment, ΔU = 0. Joule concluded that U
does not change when a gas expands isothermally and therefore that πT = 0. His
experiment, however, was crude. In particular, the heat capacity of the apparatus was
so large that the temperature change that gases do in fact cause was too small to measure.
Nevertheless, from his experiment Joule had extracted an essential limiting
property of a gas, a property of a perfect gas, without detecting the small deviations
characteristic of real gases.