For the calculation of sonic velocities or changes in pressure, volume, or temperature in gases, the isentropic or polytropic exponent of the gas or gas mixture must be known. So far it has been needed also for designing supersonic expansion nozzles. However, it is shown in this paper that more accurate designs of such nozzles can be obtained without the use of the isentropic or polytropic exponent. As long as no chemical reaction occurs in the gas, the isentropic exponent is equal to the ratio of the specific heat at constant pressure to that at constant volume. However, in jet engines or in hypersonic wind tunnels using very high stagnation temperatures, the isentropic exponent is no longer identical to the ratio of the specific heats because of the energy released or absorbed by the chemical reactions. Methods are presented for calculating differential and integral values of the isentropic exponents in gases without and with consideration of chemical reactions. A numerical evaluation of the method is given for dissociating hydrogen. The results of this investigation indicate that the isentropic exponent of a chemically reacting gas mixture differs greatly from the ratio of the specific heats. It is also shown that accurate designs of supersonic expansion nozzles for chemically reacting gases require a detailed thermodynamic analysis of the system.

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