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 given by $ p = mv $, and kinetic energy $ KE $ is given by $ KE = \frac{1}{2}mv^2 $. If momentum is doubled, $ 2p = 2mv $, then velocity $ v $ is doubled. Substituting $ 2v $ into the kinetic energy equation gives $ KE = \frac{1}{2}m(2v)^2 = 4 \times \frac{1}{2}mv^2 $, so kinetic energy increases 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 $\sqrt { 2 }$