  We consider the critical system with a point defect and study the variation
of thermodynamic quantities, which are the differences between those with and
without the defect. Within renormalization group theory, we show generally that
the critical exponent of the internal energy variation is the specific heat
exponent of a pure system, and the critical exponent of the heat capacity
variation is that for the temperature derivative of specific heat of a pure
system. This conclusion is valid for the isotropic systems with a short-range
interaction. As an example we solve the two dimensional Ising model with a
point defect numerically. The variations of the free energy, internal energy
and specific heat are calculated with bond propagation algorithm. At the
critical point, the internal energy variation diverges with the lattice size
logarithmically and the heat capacity variation diverges with size linearly.
Near the critical point, the internal energy variation behaves as $\ln |t|$ and
the heat capacity variation behaves as $|t|^{-1}$, where $t$ is the reduced
temperature.
