If at $STP$,the velocity of sound in a gas $(\gamma = 1.5)$ is $600 \, m/s$,the $r.m.s.$ velocity of the gas molecules at $STP$ will be ........... $m/s$.

$V_{rms}$ denotes the root mean square speed,$\bar{V}$ the average speed,and $V_m$ the most probable speed of gas molecules. Which of the following is the correct relationship?

Select the incorrect statement about Maxwell's speed distribution.

$A$ 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:

By what factor will the $r.m.s.$ velocity change if the temperature is raised from $27^\circ C$ to $327^\circ C$?

To increase the rms speed of gas molecules by $25 \%$,the percentage increase in absolute temperature of the gas is to be