Molecules in a spherical container make wall collisions in a great circle plane of the sphere. All paths traveled between collisions are equal in length. (a) Relate the path length Al to the angle 0 and the sphere radius r. (b) Express the component of the molecular momentum transferred to the wall in a collision in terms of the molecular mass m, the speed v, and the angle 0. (c) Using parts (a) and (b), calculate the average force exerted on the wall by one molecule. (d) Derive the relation PV = PV = } Nmv² for a spheri- cal container. This is the same relation found for a rectangular box in Section 9.5.

Molecules in a spherical container make wall collisions in a great circle plane of the sphere. All paths traveled between collisions are equal in length. (a) Relate the path length Al to the angle 0 and the sphere radius r. (b) Express the component of the molecular momentum transferred to the wall in a collision in terms of the molecular mass m, the speed v, and the angle 0. (c) Using parts (a) and (b), calculate the average force exerted on the wall by one molecule. (d) Derive the relation PV = PV = } Nmv² for a spheri- cal container. This is the same relation found for a rectangular box in Section 9.5.