A 0.25 g single crystal of Bi2Sr2CaCu2O8 with a sharp superconducting transition at 85 K is characterized by AC susceptibility, X-ray diffraction, Meissner effect, normal-state susceptibility, magnetization in the mixed state, and specific heat from 1 to 300 K. The residual linear term γ∗T in the specific heat at low T is small and field independent. High-resolution (<0.02%) adiabatic specific heat experiments performed between 0 and 14 T near tc show that: (a) there is no mean-field specific heat jump at Tc; (b) a symmetrical logarithmic ‘divergence' occurs at the transition; (c) its amplitude decreases with B; (d) its width scales with B; (e) Tc does not depend on the field, and coincides with the crossing point of the magnetization curves M∗(H, T∗); (f) a crossing point Cx (H, Tx) is found in the specific heat 10 K below Tc; (g) the effect of a field along the CuO planes is at least 50 times smaller than that of a field along the c axis; (h) no transition is observed at the irreversibility line. An empirical formula for ϑ(C/T)/ϑH that accounts for C(H, T) and M(H, T) data over a wide temperature and field range is proposed.