  We consider the capacity of entanglement as a probe of the Hawking radiation
in a two-dimensional dilaton gravity coupled with conformal matter of large
degrees of freedom. A formula calculating the capacity is derived using the
gravitational path integral, from which we speculate that the capacity has a
discontinuity at the Page time in contrast to the continuous behavior of the
generalized entropy. We apply the formula to a replica wormhole solution in an
eternal AdS black hole coupled to a flat non-gravitating bath and show that the
capacity of entanglement is saturated by the thermal capacity of the black hole
in the high temperature limit.
