Physics Puzzle: Gas Pressure

Posted on April 11, 2008
Filed Under Physics Puzzles |

After our last week’s excursion into computer science, we’re back to physics and an interesting puzzle, which I’ll split into two parts - one will be given in a few days.

An ideal gas of temperature T1 is stored in a container with walls at a fixed temperature T2. Will the pressure exerted by the gas on the container’s walls depend on T2? If not, why? If yes, will it be greater when T1>T2 or when T2>T1?

Good luck & enjoy! :)

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One Response to “Physics Puzzle: Gas Pressure”

  1. admin on April 15th, 2008 11:58 am

    SOLUTION (ADDED 15/4/2008)

    The correct answer is that the gas exerts a larger pressure when T2>T1.

    The average energy of a molecule is ~ kT, where k is Boltzmann’s constant, so (because E = 1/2*m*v^2) the average velocity of a molecule is v ~ sqrt(E) ~ sqrt(T).

    The gas continually heats up by interacting with the wall, so a molecule will get some energy from the collision. Hence, if it had a temperature T before collision, it will have a temperature T + dT after the collision, meaning its velocity will be higher. Therefore, more pressure is exerted in the T2 > T1 case, because the pressure is really just momentum being given away to the walls.

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