  In this note we investigate the first law of thermodynamics of the
two-dimensional conformal field theory (CFT) that is dual to black holes. We
start from the Cardy formula and get the CFT thermodynamics with minimal
reasonable assumptions. We use both the microcanonical ensemble and canonical
ensemble versions of the Cardy formula. In the black hole/CFT correspondence
the black hole is dual to a CFT with excitations, and the black hole mass $M$
and charge $N$ correspond to the energy and charge of the excited CFT. The CFT
left- and right-moving central charges $c_{L,R}$ should be quantized, and so we
assume that they are mass-independent. Also we assume the difference of the
left- and right-moving sector levels $N_L-N_R$ is mass-independent dual to
level matching condition. The thermodynamics of two-dimensional CFT we get is
universal and supports the thermodynamics method of black hole/CFT
correspondence.
