Question

The absolute temperature of a gas is increased to $16$ times of the original temperature. The rms speed of its molecules will become

• A. $4$ times
• B. $16$ times
• C. $64$ times
• D. $256$ times

Answer 1

Answer: (A)

$4$ times

Answer 2

Let initial absolute temperature of gas be $T$
$\therefore$ New absolute temperature of gas, $T'=16\,T$
Root mean square speed of molecules of gas is given by
$v_{rms}=\sqrt{\frac{3RT}{M}}$
$\therefore$ At new absolute temperature, $v_{rms}$ become $4$ times