Who invented kinetic theory

These can accurately describe the properties of dense gases, because they include the volume of the molecules. The necessary assumptions are the absence of quantum effects, molecular chaos and small gradients in bulk properties. Expansions to higher orders in the density are known as virial expansions. The definitive work is the book by Chapman and Enskog but there have been many modern developments and there is an alternative approach developed by Grad based on moment expansions.

This is known as the Knudsen regime and expansions can be performed in the Knudsen number. The kinetic theory has also been extended to include inelastic collisions in granular matter by Jenkins and others. Pressure is explained by kinetic theory as arising from the force exerted by gas molecules impacting on the walls of the container. Consider a gas of N molecules, each of mass m , enclosed in a cuboidal container of volume V.

When a gas molecule collides with the wall of the container perpendicular to the x coordinate axis and bounces off in the opposite direction with the same speed an elastic collision , then the momentum lost by the particle and gained by the wall is:. Now considering the total force acting on all six walls, adding the contributions from each direction we have:. Assuming there are a large number of particles moving sufficiently randomly, the force on each of the walls will be approximately the same and now considering the force on only one wall we have:.

Thus, as cross-sectional area multiplied by length is equal to volume, we have the following expression for the pressure. Also, as Nm is the total mass of the gas, and mass divided by volume is density. Note that the product of pressure and volume is simply two thirds of the total kinetic energy. Thus, the product of pressure and volume per mole is proportional to the average translational molecular kinetic energy.

The average distance that a molecule travels between collisions has come to be known as its mean free path. Clausius realized that while the mean free path must be very big compared to the actual size of the molecules, it would still have to be small enough that a fast-moving molecule would collide with other molecules many times each second Figure 3.

Thus, gas molecules are constantly colliding and changing directions. For example, at room temperature, one oxygen molecule travels an average distance of 67 nm almost 1, times narrower than the width of a human hair before colliding with another molecule. And this single molecule collides with others 7.

This astounding frequency of collisions explains how gas molecules can zip along at hundreds of meters per second, but still take minutes to cross a room. Thanks to Clausius, Langmuir understood that he needed to decrease the mean free path for the tungsten atoms sublimating off the filament. In a vacuum, the mean free path was very long, and the tungsten atoms quickly make their way from the filament to the inside of the bulb.

Only a tiny number of the gas molecules are actually moving at the slowest and fastest speeds possible—but we know now that this small number of speedy molecules are especially important, because they are the most likely molecules to undergo a chemical reaction.

Along with these ideas, Maxwell proposed that gas particles should be treated mathematically as spheres that undergo perfectly elastic collisions. This means that the net kinetic energy of the spheres is the same before and after they collide, even if their velocities change. A major use of modern KMT is as a framework for understanding gases and predicting their behavior. KMT links the microscopic behaviors of ideal gas molecules to the macroscopic properties of gases.

In its current form, KMT makes five assumptions about ideal gas molecules:. Gases consist of many molecules in constant, random, linear motion. Intermolecular forces are negligible.

In other words, collisions between molecules are perfectly elastic. The average kinetic energy of all molecules is proportional to the absolute temperature of the gas. This means that, at any temperature, gas molecules in equilibrium have the same average kinetic energy but NOT the same velocity and mass. These behaviors are common to all gases because of the relationships between gas pressure, volume , temperature, and amount, which are described and predicted by the gas laws for more on the gas laws , please see our Properties of Gases module.

But KMT and the gas laws are useful for understanding more than abstract ideas about chemistry. This means that if you took all the air from a fully inflated bike tire and put the air inside a much larger, empty car tire, the air would not be able to exert enough pressure to inflate the car tire. While this example about the relationship between gas volume and pressure may seem intuitive, KMT can help us understand the relationship on a molecular level. According to KMT, air pressure depends on how often and how forcefully air molecules collide with tire walls.

This means that there are fewer collisions per unit of time, which results in lower pressure and an underinflated car tire. While KMT is a useful tool for understanding the linked behaviors of molecules and matter , particularly gases, KMT does have limitations related to how its theoretical assumptions differ from the behavior of real matter. Real gas molecules do experience intermolecular forces.

As pressure on a real gas increases and forces its molecules closer together, the molecules can attract one another. This attraction slows down the molecules just a little bit before they slam into one another or the walls of a container, so that the pressure inside a container of real gas molecules is slightly lower than we would expect based on KMT.

Calculating an Average from a Probability Distribution. Calculating an average for a finite set of data is fairly easy. The average is calculated by. But how does one proceed when the set of data is infinite? Or how does one proceed when all one knows are the probabilities for each possible measured outcome?

It turns out that that is fairly simple too! This can also be extended to problems where the measurable properties are not discrete like the numbers that result from rolling a pair of dice but rather come from a continuous parent population.

In this case, if the probability is of measuring a specific outcome, the average value can then be determined by. A value that is useful and will be used in further developments is the average velocity in the x direction. This can be derived using the probability distribution, as shown in the mathematical development box above. This integral will, by necessity, be zero. These motions will have to cancel. Since this cannot be negative, and given the symmetry of the distribution, the problem becomes.

In other words, we will consider only half of the distribution, and then double the result to account for the half we ignored. This expression indicates the average speed for motion of in one direction.

However, real gas samples have molecules not only with a distribution of molecular speeds and but also a random distribution of directions. Using normal vector magnitude properties or simply using the Pythagorean Theorem , it can be seen that. Since the direction of travel is random, the velocity can have any component in x, y, or z directions with equal probability. As such, the average value of the x, y, or z components of velocity should be the same.

And so. All that remains is to determine the form of the distribution of velocity magnitudes the gas molecules can take. One of the first people to address this distribution was James Clerk Maxwell In his paper Maxwell, Illustrations of the dynamical theory of gases.

Part 1. On the motions and collisions of perfectly elastic spheres, , proposed a form for this distribution of speeds which proved to be consistent with observed properties of gases such as their viscosities.