The rms speed of the molecules of Hydrogen, Oxygen and Carbondioxide at the same temperature are $\mathrm{V}_{\mathrm{H}}$, $\mathrm{V}_{\mathrm{O}}$ and $\mathrm{V}_{\mathrm{C}}$ respectively then:

(B) $\mathrm{V}_{\mathrm{H}}>\mathrm{V}_{\mathrm{O}}>\mathrm{V}_{\mathrm{C}}$

(A) $\mathrm{V}_{\mathrm{C}}>\mathrm{V}_{\mathrm{O}}>\mathrm{V}_{\mathrm{H}}$

(C) $\mathrm{V}_{\mathrm{H}}=\mathrm{V}_{\mathrm{O}}=\mathrm{V}_{\mathrm{C}}$

(D) $\mathrm{V}_{\mathrm{H}}=\mathrm{V}_{\mathrm{O}}>\mathrm{V}_{\mathrm{C}}$

JEE Main · 2021 · 26 Aug 2021 · Shift 1 · Heat & Thermodynamics

The rms speed of the molecules of Hydrogen, Oxygen and Carbondioxide at the same temperature are

V_{H}

V_{O}

and

V_{C}

respectively then:

(A) $V_{C} > V_{O} > V_{H}$
(B) $V_{H} > V_{O} > V_{C}$ ✓ Correct
(C) $V_{H} = V_{O} = V_{C}$
(D) $V_{H} = V_{O} > V_{C}$

Answer: (B)

Solution

At a given temperature

v_{rms} = \frac{3 R T}{M} \Rightarrow v_{rms} \propto \frac{1}{M}

The molar masses are

2

g/mol for

H_{2}

32

g/mol for

O_{2}

and

44

g/mol for

C O_{2}

, so the lightest molecules are the fastest and the ordering is

V_{H} > V_{O} > V_{C}

JEE Main · 2021 · 26 Aug 2021 · 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 →