$N$ 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.
-(c) the greater total thermal energy $U$, and
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.
-(c) the greater total thermal energy $U$, and
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 total thermal energy $U$ of a gas is given by $U = \frac{f}{2}NkT$, where $f$ is the degrees of freedom. For a monatomic gas, $f = 3$, and for a diatomic gas at room temperature, $f = 5$. Since both gases have the same number of molecules and are at the same temperature, the diatomic gas $B$ with more degrees of freedom will have greater total thermal energy.

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