  We study the thermodynamics of Bose-Einstein condensation in a weakly
interacting quasi-homogeneous atomic gas, prepared in an optical-box trap. We
characterise the critical point for condensation and observe saturation of the
thermal component in a partially condensed cloud, in agreement with Einstein's
textbook picture of a purely statistical phase transition. Finally, we observe
the quantum Joule-Thomson effect, namely isoenthalpic cooling of an
(essentially) ideal gas. In our experiments this cooling occurs spontaneously,
due to energy-independent collisions with the background gas in the vacuum
chamber. We extract a Joule-Thomson coefficient $\mu_{\rm JT} > 10^9$ K/bar,
about ten orders of magnitude larger than observed in classical gases.
