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

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

Tardigrade Admin · Accepted Answer

Let initial absolute temperature of gas be

T

∴

New absolute temperature of gas,

T^{'} = 16 T

Root mean square speed of molecules of gas is given by

v_{r m s} = \frac{3 RT}{M}

∴

At new absolute temperature,

v_{r m s}

become

4

times

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

$4$ times

$16$ times

$64$ times

$256$ times

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

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

4 times

16 times

64 times

256 times