The temperature of an ideal gas is increased from 200 K to 800 K. If r.m.s. speed of gas at 200 K is $\mathrm{v}_{0}$. Then, r.m.s. speed of the gas at 800 K will be:

JEE Main · 2023 · 06 Apr 2023 · Shift 2 · Heat & Thermodynamics

The temperature of an ideal gas is increased from 200 K to 800 K. If r.m.s. speed of gas at 200 K is

v_{0}

. Then, r.m.s. speed of the gas at 800 K will be:

(A) $v_{0}$
(B) $4 v_{0}$
(C) $\frac{v _{0}}{4}$
(D) $2 v_{0}$ ✓ Correct

Answer: (D)

Solution

The r.m.s. speed is

v_{rms} = \frac{3 R T}{M}

, so

v_{rms} \propto T

. Raising the temperature from

200

K to

800

K multiplies

T

4

, so the speed is multiplied by

4 = 2

. The r.m.s. speed at

800

K is

2 v_{0}

JEE Main · 2023 · 06 Apr 2023 · Shift 2 · Single correct option

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