The relation between root mean square speed $\left(\mathrm{v}_{\mathrm{rms}}\right)$ and most probable speed ( $\mathrm{v}_{\mathrm{p}}$ ) for the molar mass M of oxygen gas molecule at the temperature of 300 K will be :-

(B) $\mathrm{v}_{\mathrm{rms}}=\sqrt{\frac{3}{2}} \mathrm{v}_{\mathrm{p}}$

(A) $\mathrm{v}_{\mathrm{rms}}=\sqrt{\frac{2}{3}} \mathrm{v}_{\mathrm{p}}$

(C) $\mathrm{v}_{\mathrm{rms}}=\mathrm{v}_{\mathrm{p}}$

(D) $\mathrm{v}_{\mathrm{rms}}=\sqrt{\frac{1}{3}} \mathrm{v}_{\mathrm{p}}$

JEE Main · 2022 · 25 Jun 2022 · Shift 1 · Heat & Thermodynamics

The relation between root mean square speed

(v_{rms})

and most probable speed (

v_{p}

) for the molar mass M of oxygen gas molecule at the temperature of 300 K will be :-

(A) $v_{rms} = \frac{2}{3} v_{p}$
(B) $v_{rms} = \frac{3}{2} v_{p}$ ✓ Correct
(C) $v_{rms} = v_{p}$
(D) $v_{rms} = \frac{1}{3} v_{p}$

Answer: (B)

Solution

From kinetic theory of gases:

Root mean square speed:

v_{rms} = \frac{3 R T}{M}

Most probable speed:

v_{mp} = \frac{2 R T}{M}

Taking the ratio:

\frac{v _{rms}}{v _{mp}} = \frac{3 R T / M}{2 R T / M} = \frac{3}{2}

Therefore:

v_{rms} = \frac{3}{2} v_{mp}

Answer: (B)

JEE Main · 2022 · 25 Jun 2022 · Shift 1 · Single correct option

Practise more: all JEE Main PYQs on Heat & Thermodynamics →

More JEE Main questions on Heat & Thermodynamics

A cylindrical tube $A B$ of length $l$ , closed at both ends contains an ideal gas of 1 mol having molecular weight $M$ . The tube is rotated in a horizontal plane with constant angular velocity $ω$ about an axis perpendicular to $A B$ and passing through the edge at end A, as s …
JEE Main 2026View solution →
Rods $x$ and $y$ of equal dimensions but of different materials are joined as shown in figure. Temperatures of end points $A$ and $F$ are maintained at $10 0^{\circ} C$ and $4 0^{\circ} C$ respectively. Given the thermal conductivity of rod x is three …
JEE Main 2026View solution →
The volume of an ideal gas increases 8 times and temperature becomes $(1/4)^{th}$ of initial temperature during a reversible change. If there is no exchange of heat in this process ( $Δ Q = 0$ ) then identify the gas from the following options (Assuming …
JEE Main 2026View solution →
Consider two boxes containing ideal gases A and B such that their temperatures, pressures and number densities are same. The molecular size of A is half of that of B and mass of molecule A is four times that of B. If the collision frequency in gas B is …
JEE Main 2026View solution →
An insulated cylinder of volume $60 cm^{3}$ is filled with a gas at $2 7^{\circ} C$ and 2 atmospheric pressure. Then the gas is compressed making the final volume as $20 cm^{3}$ while allowing the temperature to rise to $7 7^{\circ} C$ . The fin …
JEE Main 2026View solution →
The r.m.s speed of oxygen molecules at $4 7^{\circ} C$ is equal to that of the hydrogen molecules kept at $____$ $^{\circ} C$ . (Mass of oxygen molecule/mass of hydrogen molecule=32/2)
JEE Main 2026View solution →