  Energetics of nuclear reaction is fundamentally important to understand the
mechanism of pair instability supernovae (PISNe). Based on the hydrodynamic
equations and thermodynamic relations, we derive exact expressions for energy
conservation suitable to be solved in simulation. We also show that some
formulae commonly used in the literature are obtained as approximations of the
exact expressions. We simulate the evolution of very massive stars of ~100-320
Msun with zero- and 1/10 Zsun, and calculate further explosions as PISNe,
applying each of the exact and approximate formulae. The calculations
demonstrate that the explosion properties of PISN, such as the mass range, the
56Ni yield, and the explosion energy, are significantly affected by applying
the different energy generation rates. We discuss how these results affect the
estimate of the PISN detection rate, which depends on the theoretical
predictions of such explosion properties.
