Problem :
Samples of H_{2} and He are at the same temperature. What is the ratio of their average velocities?
The molar mass of H_{2} is half that of He. The temperatures of the two samples are the same, so their kinetic energies are the same. This leads to the following equation:
M_{H2}(V_{H2})^{2} = M_{He}(V_{He})^{2}
Rearranging and solving this equation, we find that = .
Problem :
A volume of H_{2} and an identical volume of O_{2} are at the same temperature. Plot the Maxwell-Boltzmann speed distributions for the two gases on the same graph.
Problem :
Calculate $v_{\mbox{rms}}$ for a sample of O_{2} at 300 K.
v_{rms}
=
=
=
480m/s
Remember that M must be in !
Problem :
Rank v_{rms}, , and v_{p} in order of increasing speed.
v_{p} < < v_{rms}
Problem :
Calculate the ratio of the rates of effusion of H_{2} over He.
=
=
Note that this exactly mirrors the ratio of the average velocities of the two gases.