Abstract: The shock equations with fully variable specific heat are derived from the fundamental aerothermodynamic equations,considering different specific heats across the shock.A method for their solution is provided.From the comparison between the solutions with constant and variable specific heat,it can be concluded that the former gives:(1)higher total temperature,lower total pressure;(2)higher Mach number,temperature and total pressure recovery,but lower static pressure behind the shock;(3)higher total pressure recovery of the inlet;(4)lower caught area ratio than the latter at high Mach number.