Question

By what factor does the average velocity of a gaseous molecule increase when the absolute temperature is doubled?

• A. $1.4$
• B. $2$
• C. $2.8$
• D. $4.0$

Answer 1

The correct option is A $1.4$

By a factor of 1.4 does the average velocity (v) of a gaseous molecule increases when the absolute temperature (T) is doubled.

$v\propto \sqrt{T}$

$\frac{v^{\prime }}{v}=\sqrt{\frac{T^{\prime }}{T}}$
The absolute temperature (T) is doubled.

$T^{\prime }=2T$

$\frac{v^{\prime }}{v}=\sqrt{\frac{2T}{T}}$

$\frac{v^{\prime }}{v}=\sqrt{2}$

$\frac{v^{\prime }}{v}=1.4$

Hence, the correct option is A.