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The conservation of energy to use here is the total kinetic energy plus internal energy inside the shock, not just the internal energy of a uniform-pressure core. With no radiative loss and negligible initial ambient energy,Substitute the adiabatic superbubble similarity solution and define the finite positive dimensionless integralThen $\dot{E}t=4\pi {\rho }_1{\dot{R}}^2{R}^{3}I$. Since $\dot{R}=3R/(5t)$ and $R^5={\alpha }^5(\dot{E}/{\rho }_1)t^3$,This is the energy normalization of a continuously driven spherical shock. It fixes $\alpha$ once the similarity profiles are determined. If the profiles describe only the shocked ambient layer, the energy of the interior hot bubble must also be included before using this normalization. A radiatively cooled shell has a different energy budget; its familiar numerical coefficient should not be substituted into this loss-free model.