Thanks for the recommendation! I’ll take a look.

step (1): Make a cold-(bosonic)atom cloud just above the BEC phase transition.
step (2): Make a narrow “dimple” (focused optical dipole) potential as Ketterle (http://dx.doi.org/10.1103/PhysRevLett.81.2194, I think). Now you have small BEC (a few thousand atoms, maybe more) in tight well exchanging heat
and particles with a larger bath of atoms.
step (3): Suddenly switch off all containing fields, both the magnets and the laser, let the clouds expand and then take a picture.

Now your condensate and thermal atom bath will expand at different rates, according to known laws. The expansion is driven by the energy that had previously been in the system. So by observing the size/shape/darkness of the expanded condensate you can say something its initial energy and atom number.

If you like generalising thermodynamics, then you will like this system because it doesn’t really have a pressure or volume, but the strength $A$ of the laser potential is a “mechanical” parameter analogous to volume with its own conjugate “pressure” $P$ in equations $dE = T dS + P dA + \mu dN$. When I was still a physicist, I had fun writing a thesis chapter about this system, trying to square the statmech with thermodynamics.