Momentum as a function of temperature

In summary, the conversation discusses the relationship between the pressure, volume, and temperature of an ideal gas used as propellant in a rocket. It is stated that heating the gas to nine times its original temperature will result in a nine-fold increase in pressure, but the exhaust velocity will only increase by a factor of three. This conclusion is based on a formula found in the Wikipedia article about the de Laval rocket nozzle.
  • #1
Jedi_Sawyer
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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?
 
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  • #2
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.
 

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FAQ: Momentum as a function of temperature

1. What is momentum?

Momentum is a measure of an object's motion, calculated by multiplying its mass and velocity. It is a vector quantity, meaning it has both magnitude and direction.

2. How does temperature affect momentum?

Temperature does not directly affect momentum, as it is a measure of an object's motion. However, temperature can indirectly influence momentum by affecting the speed and direction of particles in a system.

3. What is the relationship between momentum and temperature?

There is no direct relationship between momentum and temperature. However, momentum and temperature can both be used to describe the motion and energy of particles in a system.

4. How is momentum affected by temperature changes in a gas?

In a gas, temperature changes can impact momentum by altering the speed and direction of gas particles. As temperature increases, gas particles move faster and their momentum increases. Conversely, as temperature decreases, gas particles move slower and their momentum decreases.

5. Can momentum be used to measure temperature?

No, momentum is not a direct measure of temperature. However, changes in momentum can be used to indirectly infer temperature changes in a system, such as in the case of gas particles.

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