The Joule experiment was an attempt by James Joule in 1843 to determine _T)
for a gas expanding into a vacuum.
The experiment involves a system that consists of a gas-filled compartment (A) and an evacuated compartment (B), both of which are immersed in a water bath (see diagram above). When the valve between the compartments is opened, the gas expands irreversibly from A to B, doing no work in the process. Assuming that no heat transfer occurs between the system and its surroundings, the first law of thermodynamics states that 
. If there is a change in temperature of the water bath, the experiment measures the change in gas temperature with the change in gas volume at constant internal energy, i.e. _U)
, which is defined as the Joule coefficient 
:
_U\;\;\;\;\;\;\;\;(88))
To determine , we refer to eq16, where _T=-\frac{1}{\left(\frac{\partial T}{\partial U}\right)_V\left(\frac{\partial V}{\partial T}\right)_U})
. Using eq15, _T=-\left(\frac{\partial U}{\partial T}\right)_V\left(\frac{\partial T}{\partial V}\right)_U)
. Substituting eq44 and eq88 in this expression,
_T=-C_V\mu_J\;\;\;\;\;\;\;\;(89))
For an ideal gas, 
is independent of the volume of the gas, i.e. _T=0)
, because there is no intermolecular forces between the molecules (see eq43a). We would therefore expect a non-zero for a real gas. However, Joule’s experiment setup was too crude to measure a non-zero . An improved version of Joule’s experiment is the Joule-Thomson experiment.
