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I don't know if a rocket exhaust must absolutely be hotter than the environment, just at a higher pressure. If you open a gas bottle, the jet is going to be very cold, but it will produce thrust. With some quick googling, the surface pressure on venus is 90 bar, and a spacex falcon produces 350 bar in the chamber, so I think a falcon 9 could quite easily take off from the surface (ignoring the fact it would melt and the tanks might crush etc)


pV=NRT

Pressure and temperature are not independent.

"Hotter than the environment" is shorthand for "contains more energy than the output region does".




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