JEE Main · 2025 · 28 Jan 2025 · Shift 1 · Heat & Thermodynamics

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For a particular ideal gas which of the following graphs represents the variation of mean squared velocity of the gas molecules with temperature?

(A)b1fdb5fb-0abb-467f-8144-df778c21c8e7-04_234_278_386_312.jpg
✓ Correct
(B)b1fdb5fb-0abb-467f-8144-df778c21c8e7-04_237_286_383_708.jpg
(C)b1fdb5fb-0abb-467f-8144-df778c21c8e7-04_236_289_635_310.jpg
(D)b1fdb5fb-0abb-467f-8144-df778c21c8e7-04_234_286_632_708.jpg

Answer: (A)

Solution

The root-mean-square speed of an ideal gas is

v_{r m s} = \frac{3 R T}{M} ⟹ v_{r m s}^{2} = \frac{3 R}{M} T

For a particular gas, the molar mass M is fixed, so

v_{r m s}^{2}

is directly proportional to the absolute temperature T — this is a straight line through the origin with a positive slope.

JEE Main · 2025 · 28 Jan 2025 · Shift 1 · Single correct option

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