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Heat and Thermodynamics question

2023 · 25 Jan · Shift 1 · Q49

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Heat and Thermodynamics
2023 · 25 Jan · Shift 1 · Q49

Heat and Thermodynamics question

2023 · 25 Jan · Shift 1 · Q49

JEE MainPhysicsHeat and ThermodynamicsMCQ+4 / −1

The root mean square velocity of molecules of gas is

A
Proportional to temperature ( $T$ )
B
Inversely proportional to square root of temperature $\left( {\sqrt {{1 \over T}} } \right)$
C
Proportional to square of temperature ( $T^2$ )
D
Proportional to square root of temperature ( $\sqrt T$ )

View written solutionFree

Correct answer: D

For an ideal gas, the root mean square (rms) speed is given by

$v_{\text{rms}}=\sqrt{\frac{3kT}{m}}$

where:

$k$ is Boltzmann constant,
$T$ is absolute temperature,
$m$ is mass of one molecule.

From the formula,

$v_{\text{rms}} \propto \sqrt{T}$

because $3k/m$ is constant for a given gas.

Now check the options:

A: Proportional to $T$ ❌
B: Inversely proportional to $\sqrt{T}$ ❌
C: Proportional to $T^2$ ❌
D: Proportional to $\sqrt{T}$ ✅

Therefore, the correct option is D.

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