How Can I Calculate Rocket Exhaust Temperature?

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Jedi_Sawyer
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Does anybody know how or where I can find a way to figure the Exhaust Temperature of a Rocket. I am considering a problem where I assigned 1.4 atmospheres to the Inlet gas pressure at 300 degrees C.
That it exited into 1 Atmosphere at exit velocity of 325 M per second.
 
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I'm not terribly familiar with compressible fluids but I do have college physics trining.
I'm writing something not for school and I wanted subsonic rocket exhaust, and I need to know the velocity of the exhaust and it's temperature I got the formula for some idealized rocket exhaust, Ve, as a function of a lot of things such as mass flow, Temperature, molecular weight, Inlet Pressure, and Isentropic Expansion. I looked up everything for dry air, 29KG/kmol. Starting with Inlet Pressure at 1.4 Atmospheres and and outlet pressure at 1 Atm. with the inlet gas at 596 degress K, I computed 325 m/s for the exhaust speed. The Wiki article for the de Laval nozzel has an example that uses dry air and it specifies the exhaust temp but I have no idea how they computed it. It doesn't seem to be a simple adiabatic expansion thing. So that is my story.
 
One place you might look is do a search on "Gas Dynamic CO2 laser" If you can fine a good technical description, it will have a lot of info related to the energy in exhaust.