Suppose that a 1.00 cm3 box in the shape of a cube is perfectly evacuated, excep

Question

Suppose that a 1.00 cm3 box in the shape of a cube is perfectly evacuated, except for a single particle of mass 1.05 10-3 g. The particle is initially moving perpendicular to one of the walls of the box at a speed of 340 m/s. Assume that the collisions of the particle with the walls are elastic.
(a) Find the mass density inside the box.


(b) Find the average pressure on the walls perpendicular to the particle's path.


(c) Find the average pressure on the other walls.


(d) Find the temperature inside the box.
K

Discuss the assumption of elastic collisions, in light of this result.

Explanation / Answer

(a) mass density = mass of particle / volume of box = 1050 g/m^3 (b) The average pressure on the walls = 121.38 x 10^3 Pa (c) The average pressure on other walls = 0 (d) from Equipartition theorem: Temperature(T) = 2 x Kinetic Energy of particle/ k_B where, k_B = 1.38 ×10^(-23) T = 0.121380 K

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