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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
Explanation
As $v_{rms}\propto\sqrt{T}$, the key treats 'increased by 3 times' as $4v$, so $T_f=16T_i=3295^\circ C$.
Detailed Solution
$T_i=-50^\circ C=223\ K$
$v_{rms}\propto\sqrt{T}$
As $v_{rms}$ increased by 3 times, $(v_{rms})_f=4(v_{rms})_{initial}$
$T_f=16T_i=16\times223=3568\ K$
$T_f=(3568-273)^\circ C=3295^\circ C$