At $T$ $K$ temperature,the average speed of $O_2$ will be $\left( \frac{7}{4} \right)$ of the $rms$ speed of $N_2$ at $47\,^oC$. Find the value of $T$.

At what temperature $(^oC)$ is the average speed of hydrogen molecules equal to the average speed of oxygen molecules at $31^oC$?

Consider an ideal gas in a closed container at $300 \ K$. The container is then heated so that the average velocity of particles of the gas increases by a factor of $4$. What would be the final temperature (in $^{\circ} C$)?

$A$ certain amount of an ideal gas is taken from its initial state $1$ to final state $4$ through the path $1 \rightarrow 2 \rightarrow 3 \rightarrow 4$ as shown in the figure. $AB, CD, EF$ are all isotherms. If $v_p$ is the most probable speed of the molecules, then:

$A$ gas $A$ has $N$ molecules at temperature $T$ with mass $m$. Another gas $B$ has $2N$ molecules at the same temperature $T$ with mass $2m$. Both are contained in a vessel. If the $rms$ velocity of molecules of gas $B$ is $v$,and the $x$-component of the mean square velocity of molecules of gas $A$ is $w^2$,find the ratio $w^2/v^2$.

Let $\overline{V}$, $V_{\text{rms}}$, and $V_{p}$ denote the mean speed, root mean square speed, and most probable speed of the molecules each of mass $m$ in an ideal monoatomic gas at absolute temperature $T$ Kelvin. Which statement$(s)$ is/are correct?