An ideal gas is held in a container of volume V at pressure P.The rms speed of a gas molecule under these conditions is v.If now the volume and pressure are changed to 2V and 2P,the rms speed of a molecule will be:
A)1/2 v
B)v
C)2v
D)4v
E)v/4

Question

Quizplus · Accepted Answer

The rms speed of an ideal gas molecule is given by:
v=√(3kT/m)
where k is Boltzmann's constant, T is the temperature in Kelvin, and m is the mass of one molecule of the gas.

When the volume and pressure are changed to 2V and 2P, the temperature remains constant. Using the ideal gas law, PV=nRT, and keeping n (the number of gas molecules) and T constant, we find that P/V is also constant. Therefore, if V is doubled and P is doubled, the constant P/V becomes 2P/2V = P/V.

Thus, the rms speed of the gas molecules is proportional to √T/m, and since T is constant and m is also constant, the rms speed does not change. Therefore, the rms speed of a molecule will still be v, and the best choice is C) 2v.

An Ideal Gas Is Held in a Container of Volume