If you want to double the kinetic energy of a gas molecule, by what factor must you increase its momentum?
A) $\sqrt { 2 }$
B) 2
C) 2 $\sqrt { 2 }$
D) 4
E) 16

Question

Quizplus · Accepted Answer

The kinetic energy $ KE $ of a gas molecule is given by $ KE = \frac{p^2}{2m} $, where $ p $ is the momentum and $ m $ is the mass. To double the kinetic energy, $ KE' = 2 \times \frac{p^2}{2m} = \frac{(p')^2}{2m} $. Solving for $ p' $, we find $ p' = p \sqrt{2} $. Thus, the momentum must be increased by a factor of $\sqrt{2}$.

If You Want to Double the Kinetic Energy of a Gas