$N$ molecules of a monatomic gas $A$ are mixed with the same number of molecules of a diatomic gas $B$ in a container, and the mixture is held at a constant temperature $T$ (which is about equal to room temperature). The molecules of gas $A$ have mass $m_{A}$, and the molecules of gas $B$ have mass $m_{B}m_{A}$ Which gas has In each case, choose from one of the four answers below.
-(a) the greater value of $\left[v^{2}\right]_{\text {avg }}$,
A) The quantity is greater for gas $A$.
B) The quantity is greater for gas $B$.
C) The quantity is the same for both gases.
D) One does not know enough to compare the quantities.

Question

$N$ molecules of a monatomic gas $A$ are mixed with the same number of molecules of a diatomic gas $B$ in a container, and the mixture is held at a constant temperature $T$ (which is about equal to room temperature). The molecules of gas $A$ have mass $m_{A}$, and the molecules of gas $B$ have mass $m_{B}>m_{A}$ Which gas has In each case, choose from one of the four answers below.
-(a) the greater value of $\left[v^{2}\right]_{\text {avg }}$,
A) The quantity is greater for gas $A$.
B) The quantity is greater for gas $B$.
C) The quantity is the same for both gases.
D) One does not know enough to compare the quantities.

Quizplus · Accepted Answer

The average squared velocity $\left[v^{2}\right]_{\text{avg}}$ is inversely related to the mass of the gas molecules for a given temperature, according to the equipartition theorem. Since $m_{A} < m_{B}$, gas $A$'s molecules will have a greater average squared velocity.

NNN Molecules of a Monatomic Gas AAA Are Mixed with the Same Number of Molecules of a the Same

$N$ Molecules of a Monatomic Gas $A$ Are Mixed with the Same Number of Molecules of a the Same