Question

by what factor does the average velocity of a gaseous molecule increases when the temperature is doubled

Answer 1

Aapne option nhi diya tha

Answer 2

Answer:

The average velocity of a gaseous molecule increases when the temperature is doubled by the factor of 1.414.

Explanation:

The formula for average velocity is given as:

$v_{av}=\sqrt{\frac{8RT}{\pi M}}$

R = gas constant

T = Temperature of the gas

Average velocity of gas molecules at temperature = T

$v_{av}=\sqrt{\frac{8RT}{\pi M}}$..(1)

Average velocity of gas molecules at double emperature = T'= 2T

$v_{av}'=\sqrt{\frac{8RT'}{\pi M}}$

$v_{av}'=\sqrt{\frac{8R(2T)}{\pi M}}$...(2)

Dividing (1) by (2)

$\frac{v_{av}}{v_{av}'}=\frac{\sqrt{\frac{8RT}{\pi M}}}{\sqrt{\frac{8R(2T)}{\pi M}}}$

$\frac{v_{av}}{v_{av}'}=\sqrt{\frac{1}{2}}$

$v_{av}'=\sqrt{2}\times v_{av}=1.414$

The average velocity of a gaseous molecule increases when the temperature is doubled by the factor of 1.414.