Question

If temperature of a gas is increased by 4 times what will be the velocity of the gas molecules​

Answer 1

Explanation:

v(rms) of gas is directly proportional to square root of temp.

so , new velocity will be twice of the original velocity

Answer 2

Root Mean Square Velocity gets Doubled

Explanation:

Internal Energy is Given by - $\frac {1}{2} Mv^2$ which is again equal to $\frac {3}{2}RT$

M = mass of  gas

•         v = rms velocity = root mean square velocity

•         R = universal gas constant

•         T = absolute temperature of the gas

Energy of a molecule is given by : $\frac {1}{2}Mv^2 = \frac {3}{2} k_B T$

      where,  $k_B$ = Boltzmann's constant

          m = mass of a molecule.

Thus, $v = \sqrt \frac {3RT}{M}$

For a given gas,  the rms velocity depends only on the square root of the absolute temperature of the gas.

$\frac {V_2}{V_1} = \sqrt \frac {T_2}{T_1}$

= $\sqrt 4$

= 2