Performance under isentropic equilibrium and frozen expansion conditions

With the assumptions thus stated, and following the approach of (15), the theoretical calculation of the specific impulse, c, c, and cF then proceeds from the isentropic statement of the nozzle expansion process  

S e (exhaust products) = Sc (combustor products) where S is the total entropy. 

It is most convenient to carry out the determination of the performance parameters in terms of the total enthalpy of the reacting mixture and the total entropy S both quantities are computed for a definite amount of mixture. The total enthalpy is the sum of the sensible enthalpy and the chemical enthalpy. Since energy must be conserved and there is no kinetic energy change in the combustion chamber part of the motor, the total enthalpy of the incoming propellants must be equal to the total enthalpy of the product gas at the product temperature. 

The expansion with complete equilibrium is governed by the following entropy equation  

Where the k s designate the gaseous components at the nozzle exhaust and k s the condensed phases. From the product temperature and composition one can calculate the total entropy in the chamber. The unknowns in equation II. C. 4. are Te and n. Recall  

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Performance under isentropic (equilibrium and frozen) expansion conditions... 

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