Equilibrium for a System with Internal Degrees of Freedom

For the case of an ideal fluid that has ``internal degrees of freedom,'' new terms must be added to the internal energy. To illustrate this, we considered that particular case numbers of molecules of each type (of a possible number of $C$ types) was variable in each of the $j$ possible phases.

$$\input{equations/13-1A}$$ (19-1)

or in general

$$\input{equations/13-1B}$$ (19-2)

The condition that we applied to find the conditions of equilibrium [( $\ensuremath{\delta}S )_{\ensuremath{\delta}U = 0 , \; \ensuremath{\delta}V = 0} \leq 0$, or, equivalently ( $\ensuremath{\delta}U )_{\ensuremath{\delta}S = 0 , \; \ensuremath{\delta}V = 0} \geq 0$] previously were not practical. It is difficult to arrange to do experiments where $U =$ constant and $V =$ constant. They are difficult to arrange in the lab.

Question: Consider that you are doing an experiment to determine the equilibrium properties of a material? What kinds of experimental conditions would be the most straightforward to implement?