Momentum Section: Problem 5: molecule in a box A single gas molecule of mass m i

Question

Momentum Section: Problem 5: molecule in a box A single gas molecule of mass m is trapped in a box and travels back and forth with constant speedv etween opposite walls A and B a distance e apart. At each collision with a wall, the molecule reverses anging speed. Assume wall A is on the left and wall B is on the right, as shown in direction without ch the figu re below, and assume as reference a coordinate z-axis pointing to the right. o--7 Write an expression in terms of the given quantities for: a) the magnitude of the change in momentum of the molecule as it collides with wall B; b) the amount of time that elapses between collisions with wall B; c) the number of collisions per second the molecule makes with wall B; d) the change in momentum undergone by the wall B, per second, as a result of these collisions.

Explanation / Answer

a) change in momentum of the molecule on colliding wall B, = final momentum - initial momentum

= m(-v i^) - (mv i^) = -2mv i^

or magnitude momentum change = 2mv

b) T = /v + /v = 2/v

c) number of collisions per second = 1/T = v/2

d) change in momentum of wall B per second = (2mv) x v/2 = mv2/

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