Question

A single atom moves at a high rate of speed inside of a small box that is otherwise evacuated. The box is a cube, with the length of each side being L = 10 cm. The atom's collisions with the sides of the box are elastic. The force F(t) on one of the six sides is (hypothetically) monitored as a function of time, and a qualitative graph of F vs t is shown in the figure. Each narrow spike in the graph shows the force when the atom is actually bouncing, and between spikes the force goes to zero as we wait for the particle to return for its next collision. The time between spikes is 2.5 times 10^-4 s. The atom is so light that gravity can be neglected for the purposes of this discussion. (a) If the trajectory of the atom is such that it hits the side of the box head-on each time, what must its speed be? (b) If the atom is Ne, what is the impulse delivered to the atom in each collision? (c) What is the time average force on the side the box for the one atom? What is the gas pressure (in atmospheres*) if the box contains one mole of Ne atoms, each with the same F(t) versus t profile? Assume the atoms don't interact with one another. (*One atm is 1.013 times 10^5 Pa)

Answer 1

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