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An evacuated container contains air molecules at a pressure of 4.2 × 10-11 atm and room temperature (298K). Determine the mean free path of the air molecules. Considers air molecules to be spherical with a radius of 1.6 × 10-10 m.
A container of helium is at a temperature of 20°C and a pressure of 100 atm. Determine the atomic diameters moved by the helium atom in between collisions.
In a vacuum chamber, the air pressure is 1.5 × 10-12 mm of Hg at a temperature of 25°C. Calculate the i) number density and ii) mean free path of a molecule. The gas in the chamber is assumed to be monoatomic.
An eccentric scientist has built a large tank with dimensions 3.0 m × 2.0 m × 1.5 m, in which tiny, spherical, silicone particles are constantly moving around randomly due to thermal agitation. She challenges her colleagues to determine the number of particles in the tank without removing any of them or using any specialized equipment. To tackle this challenge, you decide to release many small, spherical plastic particles into the tank and measure their average distance of travel before colliding with one of the metallic particles. After conducting many trials, you find that the plastic particles travel an average distance of 1.2 m. Can you estimate the total number of silicone particles in the tank? Consider the diameter of plastic and silicone particle is 4.8 cm.
Suppose you are in a dense forest and can barely see trees that are 50 m away due to the fog. If the number of fog particles was to decrease by a factor of 3, what is the farthest distance you would be able to see through the forest? Consider the fog particles are similar to gas molecules with respect to their dependence on the number density of the gas and molecular radius.
A vacuum chamber used for scientific experiments has a diameter of 2.0 m and operates at a temperature of 25°C. The air molecules within this chamber have a diameter of 0.4 nm. At what pressure does the chamber operate to ensure an air molecule is as likely to cross the container and collide with the opposite wall as it is to collide with another air molecule?