= Solution
In the <shock frame>, integrate <mass conservation>, momentum conservation, and total-energy conservation across a thin interval containing the stationary <normal shock wave>. No mass, momentum, or energy is stored in the vanishingly thin interval, so each flux has the same value on both sides. For a <perfect gas>, the <specific enthalpy> is $h=\gamma p/[(\gamma-1)\rho]$. The resulting <Rankine-Hugoniot conditions for a perfect gas> are
$$
\boxed{\begin{aligned}
\rho_1u_1&=\rho_2u_2,\\
p_1+\rho_1u_1^2&=p_2+\rho_2u_2^2,\\
u_1\left(\frac{\rho_1u_1^2}{2}+\frac{\gamma p_1}{\gamma-1}\right)
&=u_2\left(\frac{\rho_2u_2^2}{2}+\frac{\gamma p_2}{\gamma-1}\right).
\end{aligned}}
$$
The momentum flux includes both transported momentum and <pressure> force. The energy flux includes kinetic energy and <enthalpy>, the latter accounting for internal energy and the work needed to push gas through the interval. <Entropy production> can occur inside the <normal shock wave> even though total energy is conserved.
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