The mechanical (or magnetic) energy available in principle from convection in a fluid body with an adiabatic temperature gradient is shown to be related to the convective heat transport by the efficiency of an ideal thermodynamic engine working across the adiabatic temperature difference. The temperature gradient at any level within the core is presumed to take either the adiabatic value or the diffusive gradient corresponding to the heat flux at that level, whichever is less. Then the convective power is calculable in terms of the assumed distribution of heat sources, the values of thermal conductivity K and the thermodynamic Gruneisen ratio, γ. Numerical results are presented for the case of heat sources uniformly distributed through the outer core, with γ=1.15. These indicate that with K=28Wm-1deg-1 (our preferred value) and an inner core temperature of 4000°K the thermodynamic efficiency of core convection rises from zero at a total heat generation Q0=2.5×1012W to 6.4% at Q0=7.5×1012W, but increases only slowly with further heat input. The efficiency is scaled in terms of the ratio K/Q0. The upper limit of plausible convective power in the core is about 7×1011W.