At what temperature (in $K$) is the $rms$ velocity of a hydrogen molecule equal to that of an oxygen molecule at $47^o \ C$?

For which gas is the $rms$ velocity maximum?

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 $^{\circ} C$)?

The speeds of the seven molecules are $1, 3, 5, 7, 2, 4$ and $6 \text{ km/s}$ respectively. The ratio of their r.m.s. velocity and average velocity will be

The temperature of an ideal gas is increased from $100 \ K$ to $400 \ K$. If '$x$' is the $R$.$M$.$S$. velocity of its molecules at $100 \ K$,what does it become at $400 \ K$?

$A$ vessel is partitioned into two equal halves by a fixed diathermic separator. Two different ideal gases are filled in the left $(L)$ and right $(R)$ halves. The $rms$ speed of the molecules in the $L$ part is equal to the mean speed of the molecules in the $R$ part. Then the ratio of the mass of a molecule in the $L$ part to that of a molecule in the $R$ part is