JEE Main 2021 · 24 February · evening · Single correct · +4 / −1
On the basis of kinetic theory of gases, the gas exerts pressure because its molecules :
- (a) continuously lose their energy till it reaches wall.
- (b) are attracted by the walls of container.
- (c) suffer change in momentum when impinge on the walls of container.
- (d) continuously stick to the walls of container.
Answer and solution
Answer (c) suffer change in momentum when impinge on the walls of container.
Solution
Physics sir · 4 steps
Gas pressure comes from molecules bouncing off the wall, each bounce reversing their momentum.
- One collision. A molecule of mass m hits a wall with velocity component vₓ along the normal. Kinetic theory assumes the collision is elastic, so it bounces back with -vₓ. Its momentum changes by 2mvₓ.
Δ p = mvₓ - (-mvₓ) = 2mvₓ
- Force on the wall. By Newton's second law, the wall must push on the molecule to cause this change, and by Newton's third law the molecule pushes back on the wall equally. Huge numbers of molecules hit every second, so these impulses add up to a steady force. Force per unit area is pressure.
- Check the others. Molecules do not lose energy on the way to the wall, because there are no intermolecular forces and collisions are elastic. Molecules are not attracted to the walls, and they do not stick. If they stuck, they would stop transferring momentum.
- So. The gas exerts pressure because its molecules suffer a change in momentum when they strike the walls. That is option (c).
The idea to keep. Whenever you ask where gas pressure comes from, think rate of momentum change at the wall. Elastic bounces give 2mvₓ per hit, and pressure is the total force per unit area.
Answer from the NTA final answer key. Solution by PrepWiser.