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Lesson: Root-Mean-Square Speed of Ideal Gas Particles Physics

In this lesson, we will learn how to determine the relationship between the absolute temperature of an ideal gas and the root-mean-square speed of its particles.

Lesson Plan

Students will be able to

use a model of single colliding gas particles that each transfers negligible kinetic energy in a collision with a container wall and apply the ideal gas law to show that the root-mean-square kinetic energy of a gas particle is directly proportional to the absolute temperature of an ideal gas,
use the equation in all combinations,
use the equation in all combinations.

Lesson Worksheet

Q1:

A cloud of helium gas consists of helium atoms. The atoms have a root-mean-square speed of 652 m/s and the gas exerts a pressure of 45,250 Pa. Find the volume of the gas. Use a value of kg for the mass of a helium atom. Give your answer to three decimal places.

Q2:

A cloud of hydrogen gas with a volume of 1.05 m³ consists of 4.22 moles of hydrogen atoms. The atoms have a root-mean-square speed of 983 m/s. Find the pressure of the gas to the nearest kilopascal. Use a value of 1.0079 g for the molar mass of hydrogen atom and a value of for the molar gas constant.

Q3:

A particle of mass moves at a speed between opposite faces of an empty cubic container of side length and volume , as shown in the diagram, colliding elastically with the container’s walls. The particle changes its momentum by each time it collides with a wall and the particle collides with the wall shown being hit in the diagram once every seconds.

Which of the following correctly represents the average force exerted on the wall of the container that the particle is shown colliding with due to the particle’s collisions?

Which of the following correctly represents the average pressure exerted on the wall of the container that the particle is shown colliding with due to the particle’s collisions?