Momentum as a function of temperature

[Jedi_Sawyer]

I think that the momentum achieved by a rocket in a vacuum with no gravitational forcec to consider, that uses a pressurized ideal gas as it's only propellant, stored in a chamber of fixed volume before being rocketed away. will achieve a final momentum related to the pressure and volume of the gas.

Now if I heat the gas inside the rocket so that it is on the absolute temperature scale nine times as hot as before, since the volume is constant that would mean that the pressure increased by a factor of nine I think.

My question is under these ideal conditions what will the mathematical change be between the first case of the gas at when the gas is heated to be nine. Why?

 

[Jedi_Sawyer]

For my example above of a gas being heated so that the temperature goes up by a factor of 9, I think the exhaust velocity will only go up by a factor of 3, so that for any given amount of propellant the momentum only goes up by a factor of three. I say this as the formula in the Wikipedia article about the de Laval rocket nozzle has a formula for computing the exhaust velocity and it shows it going at the sq root of the temerature.