Adopted or used LibreTexts for your course? By squaring the velocities and taking the square root, we overcome the “directional” component of velocity and simultaneously acquire the particles’ average velocity. The macroscopic phenomena of pressure can be explained in terms of the kinetic molecular theory of gases. In other words their volume is miniscule compared to the distance between themselves and other molecules. This relationship is shown by the following equation: At a given temperature, the pressure of a container is determined by the number of times gas molecules strike the container walls. As the temperature increases, the particles acquire more kinetic energy. The macroscopic phenomena of pressure can be explained in terms of the kinetic molecular theory of gases.

If the gas is compressed to a smaller volume, then the same number of molecules will strike against a smaller surface area; the number of collisions against the container will increase, and, by extension, the pressure will increase as well. Over four hundred years, scientists including Rudolf Clausius and James Clerk Maxwell developed the kinetic-molecular theory (KMT) of gases, which describes how molecule properties relate to the macroscopic behaviors of an ideal gas—a theoretical gas that always obeys the ideal gas equation.

Since the value excludes the particles’ direction, we now refer to the value as the average speed.

The significance of the above relationship is that pressure is proportional to the mean-square velocity of molecules in a given container.

Gas particles are in a constant state of random motion and move in straight lines until they collide with another body. Using the above logic, we can hypothesize the velocity distribution for a given group of particles by plotting the number of molecules whose velocities fall within a series of narrow ranges. The kinetic molecular theory contains a number of statements compatible with the assumptions of the ideal gas law. In order to apply the kinetic model of gases, five assumptions are made: The last assumption can be written in equation form as: \[KE = \dfrac{1}{2}mv^2 = \dfrac{3}{2}k_BT\]. kinetic molecular theory to the very visibly macroscopic behavior of the ideal Kinetic Molecular Theory can be used to explain both Charles’ and Boyle’s Laws. The total momentum change for this collision is then given by.
The root-mean-square speed takes into account both molecular weight and temperature, two factors that directly affect the kinetic energy of a material.

In other words, there is no net loss or gain of kinetic energy when particles collide. The root-mean-square speed is the measure of the speed of particles in a gas, defined as the square root of the average velocity-squared of the molecules in a gas. In theory, this energy can be distributed among the gaseous particles in many ways, and the distribution constantly changes as the particles collide with each other and with their boundaries. derive the ideal gas law.