A Sample of gas is held at constant pressure in a cylinder moved by a closed piston. If the volume is halved, how will the new Vrms speed compare with the old one?

Question

a) square root of 2 times greater
b) the same
c) 2 times greater
d) 4 times greater
e) none

i think its e because i think it increases by square root of .5
but i really don't know.

Answer 1

Velocity_rms = sqrt (3RT/M)
I don't see pressure anywhere in the formula. R is the same, T is the same(I assume), molar mass is the same. So Vrms must be ??

Answer 2

yes but T is affected volume and pressure changes according to the ideal gas law

Answer 3

The problem doesn't say T changes. Of course, it doesn't say it doesn't change, either. IF the volume was halved by moving the piston down then I could see that work would be done on the gas and T would increase. But the problem says the P stays constant and the volume is somehow (and miraculously) halved so I don't see how any work could be done on the gas. And no work, T should stay the same. The problem just isn't clear on that. You are right, however, the correct answer depends upon how T is treated.