The specific heat of the superconducting cuprates is calculated over the entire phase diagram. A d-wave BCS approach based on the large Fermi surface of Fermi liquid and band structure theory provides a good description of the overdoped region. At underdoping it is essential to include the emergence of a second energy scale, the pseudogap and its associated Gutzwiller factor, which accounts for a reduction in the coherent piece of the electronic Greens function due to increased correlations as the Mott insulating state is approached. In agreement with experiment, we find that the slope of the linear in T dependence of the low temperature specific heat rapidly increases above optimum doping while it is nearly constant below optimum. Our theoretical calculations also agree with recent data on Bi$_2$Sr$_{2-rm x}$La$_{rm x}$CuO$_{6+delta}$ for which the normal state is accessed through the application of a large magnetic field. A quantum critical point is located at a doping slightly below optimum.
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