At what temperature is the $R$.$M$.$S$. velocity of a hydrogen molecule equal to that of an oxygen molecule at $47^{\circ} C$ (in $K$)? (Molecular weight of hydrogen $= 2$,molecular weight of oxygen $= 32$)

The speed distribution for a sample of $N$ gas particles is shown below. $P(v) = 0$ for $v > 2 v_0$. How many particles have speeds between $1.2 v_0$ and $1.8 v_0$ (in $N$)?

The temperature of a gas is $-68^{\circ} C$. To what temperature should it be heated,so that the r.m.s. velocity of the molecules be doubled (in $^{\circ} C$)?

Three closed vessels $A, B$ and $C$ are at the same temperature $T$ and contain gases. Vessel $A$ contains only $O_2$,vessel $B$ contains only $N_2$,and vessel $C$ contains a mixture of equal quantities of $O_2$ and $N_2$. If the rms speed of $O_2$ molecules in vessel $A$ is $v_1$ and that of $N_2$ molecules in vessel $B$ is $v_2$,then the rms speed of $O_2$ molecules in vessel $C$ is:

The rms speed of an oxygen molecule in a vessel at a particular temperature is $\left(1+\frac{5}{x}\right)^{\frac{1}{2}} v$,where $v$ is the average speed of the molecule. The value of $x$ will be: (Take $\pi=\frac{22}{7}$)

The effect of temperature on Maxwell's speed distribution is correctly shown by