JEE Main 2026 — Physics Thermodynamics

2026mcqmedium

The mean free path of a molecule of diameter $5 \times 10^{-10} \mathrm{~m}$ at the temperature $41^{\circ} \mathrm{C}$ and pressure $1.38 \times 10^{5} \mathrm{~Pa}$ , is given as $\_\_\_\_$ m. (Given $k_{B}=1.38 \times 10^{-23} \mathrm{~J} / \mathrm{K}$ ).

Official previous-year question

Held on 28 Jan 2026 · Verified 6 Jul 2026.

Options

A
$10 \sqrt{2} \times 10^{-8}$
B
$2 \sqrt{2} \times 10^{-8}$
C
$2 \sqrt{2} \times 10^{-10}$
D
$2 \times 10^{-8}$

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Solution

Mean free path is calculated using $\lambda = \frac{k_B T}{\sqrt{2} \pi d^2 P}$

Given: $d = 5 \times 10^{-10}$ m, $T = 41°C = 314$ K, $P = 1.38 \times 10^5$ Pa, $k_B = 1.38 \times 10^{-23}$ J/K

$\lambda = \frac{1.38 \times 10^{-23} \times 314}{\sqrt{2} \times \pi \times (5 \times 10^{-10})^2 \times 1.38 \times 10^5}$

$= \frac{1.38 \times 10^{-23} \times 314}{\sqrt{2} \times \pi \times 25 \times 10^{-20} \times 1.38 \times 10^5}$

Numerator: $433.32 \times 10^{-23}$

Denominator: $1.414 \times 3.14159 \times 34.5 \times 10^{-15} = 153.18 \times 10^{-15}$

$\lambda = \frac{433.32 \times 10^{-23}}{153.18 \times 10^{-15}} = 2.83 \times 10^{-8}$ m = $2\sqrt{2} \times 10^{-8}$ m

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Solution

Mean free path is calculated using $\lambda = \frac{k_B T}{\sqrt{2} \pi d^2 P}$

Given: $d = 5 \times 10^{-10}$ m, $T = 41°C = 314$ K, $P = 1.38 \times 10^5$ Pa, $k_B = 1.38 \times 10^{-23}$ J/K

$\lambda = \frac{1.38 \times 10^{-23} \times 314}{\sqrt{2} \times \pi \times (5 \times 10^{-10})^2 \times 1.38 \times 10^5}$

$= \frac{1.38 \times 10^{-23} \times 314}{\sqrt{2} \times \pi \times 25 \times 10^{-20} \times 1.38 \times 10^5}$

Numerator: $433.32 \times 10^{-23}$

Denominator: $1.414 \times 3.14159 \times 34.5 \times 10^{-15} = 153.18 \times 10^{-15}$

$\lambda = \frac{433.32 \times 10^{-23}}{153.18 \times 10^{-15}} = 2.83 \times 10^{-8}$ m = $2\sqrt{2} \times 10^{-8}$ m

JEE Main 2026 — Physics Thermodynamics

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JEE Main 2026 — Physics Thermodynamics

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Solution

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JEE Main Thermodynamics in other years

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Other Physics topics for JEE Main

Mechanics

Electromagnetism

Modern Physics

Optics

Waves & Oscillations

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