Specific heat measurements performed on high purity vapor-grown Nb_3Sn crystals show clear features related to both the martensitic and superconducting transitions. Our measurements indicate that the martensitic anomaly does not display hysteresis, meaning that the martensitic transition could be a weak first or a second order thermodynamic transition. Careful measurements of the two transition temperatures display an inverse correlation between both temperatures. At low temperature specific

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... t measurements show the existence of a single superconducting energy gap feature.