# What is the relationship between pressure and kinetic energy

### Pressure is Confined Kinetic Energy

Kinetic Molecular Theory Postulates, How the Kinetic Molecular Theory Explains the The pressure of a gas results from collisions between the gas particles and the This relationship eventually became known as Graham's law of diffusion. Pressure of a gas is one thing and its kinetic energy is another. From the kinetic theory of gas, prove that P=2/3, where E is kinetic energy per unit volume of the gas? The pressure p of an ideal gas and its mean K.E., per unit volume are related by what relation?. If temperature and pressure are both the kinetic energy of the Each one has its separate definition, and the relationships between them must.

This means that the equations of motion of the molecules are time-reversible. The average kinetic energy of the gas particles depends only on the absolute temperature of the system. The kinetic theory has its own definition of temperature, not identical with the thermodynamic definition. The elapsed time of a collision between a molecule and the container's wall is negligible when compared to the time between successive collisions.

There are negligible gravitational force on molecules. More modern developments relax these assumptions and are based on the Boltzmann equation. 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. An important book on kinetic theory is that by Chapman and Cowling.

This is known as the Knudsen regime and expansions can be performed in the Knudsen number. Equilibrium properties[ edit ] Pressure and kinetic energy[ edit ] In kinetic model of gases, the pressure is equal to the force exerted by the atoms hitting and rebounding from a unit area of the gas container surface.

There is no change in the speed with which the particles move, but the container is smaller. Thus, the particles travel from one end of the container to the other in a shorter period of time. This means that they hit the walls more often.

Any increase in the frequency of collisions with the walls must lead to an increase in the pressure of the gas.

Thus, the pressure of a gas becomes larger as the volume of the gas becomes smaller. Charles' Law V T The average kinetic energy of the particles in a gas is proportional to the temperature of the gas.

Because the mass of these particles is constant, the particles must move faster as the gas becomes warmer. If they move faster, the particles will exert a greater force on the container each time they hit the walls, which leads to an increase in the pressure of the gas. If the walls of the container are flexible, it will expand until the pressure of the gas once more balances the pressure of the atmosphere.

The volume of the gas therefore becomes larger as the temperature of the gas increases. Avogadro's Hypothesis V N As the number of gas particles increases, the frequency of collisions with the walls of the container must increase.

This, in turn, leads to an increase in the pressure of the gas.

Flexible containers, such as a balloon, will expand until the pressure of the gas inside the balloon once again balances the pressure of the gas outside. Thus, the volume of the gas is proportional to the number of gas particles.

Imagine what would happen if six ball bearings of a different size were added to the molecular dynamics simulator. The total pressure would increase because there would be more collisions with the walls of the container. But the pressure due to the collisions between the original ball bearings and the walls of the container would remain the same.

There is so much empty space in the container that each type of ball bearing hits the walls of the container as often in the mixture as it did when there was only one kind of ball bearing on the glass plate. The total number of collisions with the wall in this mixture is therefore equal to the sum of the collisions that would occur when each size of ball bearing is present by itself.

In other words, the total pressure of a mixture of gases is equal to the sum of the partial pressures of the individual gases. Graham's Laws of Diffusion and Effusion A few of the physical properties of gases depend on the identity of the gas. One of these physical properties can be seen when the movement of gases is studied.

In Thomas Graham used an apparatus similar to the one shown in the figure below to study the diffusion of gases the rate at which two gases mix. This apparatus consists of a glass tube sealed at one end with plaster that has holes large enough to allow a gas to enter or leave the tube. When the tube is filled with H2 gas, the level of water in the tube slowly rises because the H2 molecules inside the tube escape through the holes in the plaster more rapidly than the molecules in air can enter the tube.

By studying the rate at which the water level in this apparatus changed, Graham was able to obtain data on the rate at which different gases mixed with air. Graham found that the rates at which gases diffuse is inversely proportional to the square root of their densities.

### Skeptic's Play: Temperature, pressure, and kinetic energy

But most of the time, as one increases, the other two also increase. As one decreases, so do the other two. This relationship is contained in the famous ideal gas law: So given a constant amount of gas in a container of constant volume, the pressure is proportional to temperature.

Somewhat less well-known is the Equipartition Theorem: U represents the total energy. In an ideal gas, all the energy is kinetic energy. So given a constant amount of gas, the kinetic energy is also proportional to temperature. But the ideal gas law and the equipartition theorem do not define temperature, pressure, or kinetic energy.

Each one has its separate definition, and the relationships between them must be derived from other principles. Therefore, it makes sense to say that there are some situations where the relationships between the three are less clear-cut.

• Kinetic theory of gases
• Kinetic Theory of Gases

As it says in the name, the ideal gas law is an idealized model of gases, and it may not hold true if there are further complicating factors. For example, if the gas is so dense that it condenses into liquid nitrogen, then the ideal gas law is obviously not going to hold. In the longer explanation, I would have to actually explain what these three things are. In order from simplest to most difficult.