RMS, Most Probable and Average Speed

The ratio amongst most probable velocity, mean velocity and root mean square velocity is given by

Assertion: Consider a system of gas having N molecules; Instantaneous K.E. of few molecules can be greater than average K.E. of the molecules of the given gas.

Reason: Number of molecules having most probable speed is greater than number of molecules having average speed.

The gas having average speed four times as that of $\mathrm{S}{\mathrm{O}}_2$ (molecular mass 64) at the same temperature, is

Let $\overline{v}$, v_rms and v_p respectively denote the mean speed, the root-mean-square speed, and the most probable speed of the molecules in an ideal monoatomic gas at absolute temperature T. The mass of a molecules is m -

The rms speed of hydrogen is $\sqrt{7}$ times the rms speed of nitrogen. If $T$ is the temperature of the gas, then

An ideal gas is maintained at constant pressure. If the temperature of an ideal gas increases from $100 K to 10000 K$.What affect does it cause on the rms Speed?

Which of the following gases will have least rms speed at a given temperature?

Which of the following statement is wrong about Maxwell's distribution curve?

What happens when the gas becomes hotter?

How can we find the most probable speed of molecules using maxwell's distribution curve for velocities of molecules of a gas?

Area under maxwell distribution represents the number of number of molecules per unit volume.

The velocity of five particles in $\mathrm{m} {\mathrm{s}}^{-1}$ are $3, 9, 4, \sqrt{15}, 2$. Calculate r.m.s. speed in $\mathrm{m} {\mathrm{s}}^{-1}$.

The root mean square velocity of a perfect gas is

The root mean square velocity of a gas molecule at $27 \mathrm{℃}$ is $1365 \mathrm{m} {\mathrm{s}}^{-1}$. The gas is

At what temperature is the root mean square speed of oxygen atom equal to the root mean square speed of helium gas atom at $-10 \mathrm{℃}$? Atomic mass of oxygen $=32$ and that of helium $=4$.

Explain Maxwell distribution of molecular speeds with necessary graph. 

Ratio of  Average velocity $\left(u_{\mathrm{av}}\right)$_, most probable velocity _{$\left({\mathrm{u}}_{\mathrm{mp}}\right)$} and root mean square velocity _{$\left({\mathrm{u}}_{\mathrm{rms}}\right)$} of a gas at a given temperature is

(Take $\pi =\frac{22}{7}$)

In case of gases, which is greater: mean value of velocities or r.m.s. value of velocities?
(Choose from: mean value/ rms value)

The average velocity of an ideal gas molecule at $27 °\mathrm{C}$ is $0.3 \mathrm{m}/\mathrm{s}$. The average velocity at $927 °\mathrm{C}$ will be

The ratio of root mean square velocity to the average velocity of a gas molecule, at a particular temperature is