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Phase transitions are well understood and generally followed by the behaviorof the associated thermodynamic quantities, such as in the case of the$\lambda$ point superfluid transition of liquid helium, which is observed inits heat capacity. In the case of a trapped Bose-Einstein condensate (BEC), theheat capacity cannot be directly measured. In this work, we present a techniqueable to determine the global heat capacity from the density distribution of aweakly interacting gas trapped in an inhomogeneous potential. This approachrepresents an alternative to models based on local density approximation. Bydefining a pair of global conjugate variables, we determine the total internalenergy and its temperature derivative, the heat capacity. We then apply thetechnique to a trapped $^{87}$Rb BEC a $\lambda$-type transition dependent onthe atom number is observed, and the deviations from the non-interacting, idealgas case are discussed. Finally we discuss the chances of using this method tostudy the heat capacity at $T \rightarrow 0$.

Measuring The Heat Capacity in a Bose-Einstein Condensation using Global Variables