Rate of particle collisions with walls with decrease in temperature and volume.

[Silversonic]

Homework Statement

A sample of gas (H2) is kept within a container with a piston seal (of mass M) at the top. This piston can move freely. Let's say the pressure on the piston above it is one atmosphere.

If we then put this container in a reservoir of ice then the volume of the gas will decrease, and we wait for its temperature to reduce to 0 degrees C. The final pressure of the gas must be the same as the initial pressure to be able to balance the forces due to the air pressure and the piston's weight.

Now I'm asked if the number of particles per unit area per unit time incident on the walls of the cylinder containing the gas will increase, decrease or stay the same after this decrease in temperature.I'm not sure how to deduce this. The average speed of the molecules will decrease due to a lower temperature, but also due to a decreased volume containing the gas the distance between the walls also lowers. I know that the pressure is the same in either case. And that the time between collisions of the walls for a single molecules is 2l/v where l is the distance between the walls and v is the molecule's velocity. But since both l and v decrease, how do I deduce if it's greater, lower or the same?

If anyone needs a diagram because my explanation is poor. Please let me know.

 

[NateD]

Homework Equations P = F/AThe Attempt at a SolutionI think that the number of molecules per unit area per unit time incident on the walls of the cylinder containing the gas will stay the same after this decrease in temperature. The pressure of the gas must remain the same in order to balance the forces due to the air pressure and the piston's weight, so the force per unit area should remain constant. Since the force is constant, the number of molecules per unit area per unit time incident on the walls of the cylinder can also remain constant. The average speed of the molecules will decrease due to a lower temperature, but also due to a decreased volume containing the gas the distance between the walls also lowers. As a result, the time between collisions of the walls for a single molecules decreases, but the number of collisions remains the same since the pressure is the same in either case.