We present new specific heat data for Nb3Sn, a well-known technically applied superconductor with a critical temperature T_c ~ 18 K, in the temperature range from 1.2 to 200 K in zero magnetic field, and from 1.5 to 22 K in fields H <= 16 T. The particularly dense and homogeneous polycrystalline sample used for this study is characterized in detail. We determine the bulk upper critical field H_c2(T) from specific heat data, and the Sommerfeld constant Gamma from the entropy S(T). We investigate in detail a low-temperature anomaly already noticed in previous investigations in zero field, and find that this feature can be quantitatively ascribed to the presence of a second superconducting gap 2 Delta_S(0) ~ 0.8 k_B T_c, in addition to the main one 2 Delta_L(0) ~ 4.9 k_B T_c. The signature of this minor gap, which affects 7.5% of the electronic density-of-states, vanishes in fields above ~ 7 T.
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