Pressure of gas when temperature and volume increases

[sgstudent]

Homework Statement

A syringe contains gas at the same pressure as the air outside. The piston moves freely along the cylinder without any friction. No gas escapes. As the syringe is heated from 20 degrees to 100 degrees the piston moves outwards. It stops moving when the temperature is steady. State how the value of each of the following quantities compares at 100 degrees, after the piston stops with its value at 20 degrees.
average distance - increased
pressure after it stops - same
average speed of gas - increased
frequency of collisions of the gas on the piston - same

Homework Equations

none

The Attempt at a Solution

i don't understand why the frequency of collision of the gas on the piston remains the same. Since at 100 degrees the pressure is the same as it was previously so shouldn't the frequency of collision be the smaller as average speed of gas increases, in order for the pressure to remain the same the frequency of collision must be smaller?

thanks for the help!

 

[ehild]

Think: The length of the cylinder increases so the molecules need longer time to get back to the piston.

ehild

 

[sgstudent]

Think: The length of the cylinder increases so the molecules need longer time to get back to the piston.

ehild

but the formula is Force on the wall = frequency * impulse of collision so if impulse increase won't frequency decrease?

 

[ehild]

You are right, the average force is impulse of the collision multiplied by the collision frequency. The pressure is the same, so the average force is the same, but the speed of the molecules is greater at higher temperature, the impulse is greater, so the frequency decreases.
Also, the length of the cylinder increases with the temperature, the speed of the molecules also increases, but the length is proportional to the temperature T and the speed is proportional to the square root of T, so the time between two collisions increases, the frequency decreases.

ehild

 

[sgstudent]

You are right, the average force is impulse of the collision multiplied by the collision frequency. The pressure is the same, so the average force is the same, but the speed of the molecules is greater at higher temperature, the impulse is greater, so the frequency decreases.
Also, the length of the cylinder increases with the temperature, the speed of the molecules also increases, but the length is proportional to the temperature T and the speed is proportional to the square root of T, so the time between two collisions increases, the frequency decreases.

ehild

But why did the answer key from O levels put it as same? Are they wrong?

 

[ehild]

It happens quite frequently that the "official" answers are wrong. I hope that is the case now, and we are right.

ehild

 

[sgstudent]

It happens quite frequently that the "official" answers are wrong. I hope that is the case now, and we are right.

ehild

ok thanks for the help! i hope we are right too