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We calculate the energy gap (latent heat) and pressure gap between the hotand cold phases of the SU(3) gauge theory at the first order deconfining phasetransition point. We perform simulations around the phase transition point withthe lattice size in the temporal direction Nt=6, 8 and 12 and extrapolate theresults to the continuum limit. We also investigate the spatial volumedependence. The energy density and pressure are evaluated by the derivativemethod with non-perturabative anisotropy coefficients. We adopt a multi-pointreweighting method to determine the anisotropy coefficients. We confirm thatthe anisotropy coefficients approach the perturbative values as Nt increases.We find that the pressure gap vanishes at all values of Nt when thenon-perturbative anisotropy coefficients are used. The spatial volumedependence in the latent heat is found to be small on large lattices.Performing extrapolation to the continuum limit, we obtain $ \Delta\epsilon/T^4 = 0.75 \pm 0.17 $ and $ \Delta (\epsilon -3 p)/T^4 = 0.623 \pm0.056.$

Latent heat at the first order phase transition point of SU(3) gauge theory