Frequency of collisions of the gas

[DeathKnight]

Some gas is put into a gas syringe with a frictionless piston which does not allow the escape of any gas. The gas is initially at 20C and is then heated to 100C. The piston is allowed to move. At 100C a time will come when the piston will stop moving outwards and become stationary(this will happen when the inner pressure is equal to atmospheric pressure). The question is: will the frequency of collisions of the gas molecules with the piston at 100C be greater, lower or same when it is compared to the frequency of collision at 20C.

 

[whozum]

Its asking you about the pressure in relation to temperature. What is the relationship between the two?

 

[DeathKnight]

They are directly proportional. I know that the pressure will increase but since the piston is friction less it will move outwards until the pressure inside the syringe is same as it is outside the syringe. But that's not my question.

 

[whozum]

Since the temperature increased,the average kinetic energy of the gas molecules ________ and therefore their velocities ________. (increase/decrease)

The pressure increases which means there are _____ (more/less) collisions per unit area than the initial pressure&volume.

The pressure increase causes the volume to ________ (increase/decrease) until the pressure is at 1atm. Therefore the surface area of the piston has _______ (inc/dec).


Tie #2 and #3 together to find your result.

 

[DeathKnight]

Thanks a lot for your replies whozum. But I really don't think I'm getting you. Can you please provide some explanation. I shall be very thankful to you if do so. :)
I personnaly think that the freqency of collisions will be reduced. My teacher says it won't be reduced infact it will remain the same. He says that the increased speed of the molecules will compensate for the increased volume. I totally agree but I can use the same explanation to show that the frequency of collision will be reduced.
At 100C the average KE of the molecules will be greater than it is at 20C. It means that the molecules of gas will move faster. As a result when they willl hit the piston with greater force. Now if the frequency of collsions of the particles with the piston remains same the force per unit area is increased as a result the pressure increases. So I think the frequency of collision should decrease to compensate for the increased force with which the molecules hit the inner walls of the piston.

 

[whozum]

Now if the frequency of collsions of the particles with the piston remains same the force per unit area is increased as a result the pressure increases. So I think the frequency of collision should decrease to compensate for the increased force with which the molecules hit the inner walls of the piston.


This is correct, but your missing the idea that the local pressure to a point is increased due to the higher pressure, but then there is a much larger surface area due to the expansion of volume, so the net change is in effect zero. The certain point will not be hit as much as the molecules will have a larger region to travel through, and more points to collide with.

 

[DeathKnight]

Now I get it. Thanks a lot whozum.