2023 Kinetic TheorySpeed of Gas Molecules (RMS Speed) Medium Question 7 of 34 in Kinetic Theory

The temperature of a gas is $-50^\circ C$. To what temperature the gas should be heated so that the rms speed is increased by 3 times?

A 223 K
B $669^\circ C$
C $3295^\circ C$
D 3097 K

The answer is C.

Solution

As $v_{rms}\propto\sqrt{T}$, the key treats 'increased by 3 times' as $4v$, so $T_f=16T_i=3295^\circ C$.

$T_i=-50^\circ C=223\ K$ $v_{rms}\propto\sqrt{T}$ As $v_{rms}$ increased by 3 times, $(v_{rms})_f=4(v_{rms})_{initial}$ $T_f=16T_i=16\times223=3568\ K$ $T_f=(3568-273)^\circ C=3295^\circ C$

Concept rms speed ∝ √T

Kinetic Theory in past papers

34 questions from this chapter have appeared across 19 exam years.