If the $rms$ speed of hydrogen gas is equal to the $rms$ speed of oxygen gas at $47^{\circ}C$,find the temperature of the hydrogen gas in $K$.

When the rms velocity of a gas is denoted by $V$,which of the following relations is true? ($T=$ absolute temperature of the gas)

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 $rms$ speed of a gas at room temperature of $27^{\circ}C$ is found to be $412 \ m/s$. The gas is:

$A$ flask contains argon and chlorine in the ratio of $2:1$ by mass. The temperature of the mixture is $27^{\circ}\text{C}$. The ratio of root mean square speed of the molecules of the two gases $\left(\frac{v_{\text{rms}}^{\text{Ar}}}{v_{\text{rms}}^{\text{Cl}}}\right)$ is : (Atomic mass of argon $= 40.0 \text{u}$ and molecular mass of chlorine $= 70.0 \text{u}$)

The temperature at which the rms speed of oxygen molecules is $75 \%$ of the rms speed of nitrogen molecules at a temperature of $287^{\circ} C$ is: (in $^{\circ} C$)