JEE Main 2025 Jan 28 Shift 1, Physics Q9: Kinetic Theory of an Ideal Gases

JEE Main2025Jan 28, Shift 1Physics

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

Solution

For an ideal gas, the root-mean-square speed is $v_{rms} = \frac{3 R T}{M}$ .

Squaring: $v_{rms}^{2} = \frac{3 R T}{M}$ .

So $⟨ v^{2} ⟩$ depends linearly on $T$ , with slope $\frac{3 R}{M}$ and zero intercept.

$∴$ The graph is a straight line through the origin (Option 1).

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