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

Question

Quizplus · Accepted Answer

Momentum $ p $ is related to kinetic energy $ KE $ by the equation $ KE = \frac{p^2}{2m} $. To double the momentum, $ p $ becomes $ 2p $. Substituting $ 2p $ into the equation gives $ KE' = \frac{(2p)^2}{2m} = \frac{4p^2}{2m} = 4 \times \frac{p^2}{2m} = 4 \times KE $. Thus, the kinetic energy must be increased by a factor of 4.

If You Want to Double the Momentum of a Gas 2\sqrt { 2 }2​

If You Want to Double the Momentum of a Gas $\sqrt { 2 }$