# Volume and kinetic energy relationship

### The Kinetic Molecular Theory Define thermal energy. Calculate the kinetic energy of a gas molecule, given its temperature. Describe the relationship between the temperature of a gas and the kinetic energy of atoms and molecules. is the volume of gas in the container, N . Demonstrate the relationship between kinetic energy and molecular speed. by gas molecules is negligible relative to the total volume of their container. The kinetic theory of gases describes a gas as a large number of submicroscopic particles This smallness of their size is such that the total volume of the individual gas molecules added up is negligible compared to the volume of the smallest open .. The relation depends on shape of the potential energy of the molecule.

This means the molecules are considered to be perfectly spherical in shape and elastic in nature. Except during collisions, the interactions among molecules are negligible. That is, they exert no forces on one another. Relativistic effects are negligible. Quantum-mechanical effects are negligible. This means that the inter-particle distance is much larger than the thermal de Broglie wavelength and the molecules are treated as classical objects.

Because of the above two, their dynamics can be treated classically. 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.

## Kinetic molecular theory of gases

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.

• Kinetic theory of gases
• Kinetic Theory of Gases

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. Graham's Law states that the rate of effusion of two different gases at the same conditions are inversely proportional to the square roots of their molar masses as given by the following equation: However, the net rate at which gas molecules move depend on their average speed.

By examining the equation above, we can conclude that the heavier the molar mass of the gas molecules slower the gas molecules move. And conversely, lighter the molar mass of the gas molecules the faster the gas molecules move. Limitations of Graham's Law Graham's Law can only be applied to gases at low pressures so that gas molecules escape through the tiny pinhole slowly. In addition, the pinhole must be tiny so that no collisions occur as the gas molecules pass through. Molecular Effusion The random and rapid motion of tiny gas molecules results in effusion.

Effusion is the escape of gas molecules through a tiny hole or pinhole. Illustration of gas molecules escaping through a small opening.

### Kinetic theory of gases - Wikipedia

This is a phenomenon called effusion. The behavior of helium gas in balloons is an example of effusion. The balloons are made of latex which is porous material that the small helium atom can effuse through. The helium inside a newly inflated balloon will eventually effuse out. This is the reason why balloons will deflate after a period of time. Molecular speeds are also used to explain why small molecules such as He diffuse more rapidly than larger molecules O2.

The escaping of helium molecules from an inflated balloon causes the deflation of the balloon after a period of time. The effusion rate, r, is inversely proportional to the square root of its molar mass, M. From the equation above, Rates of effusion of two gases The relative rates of effusion of two gases at the same temperature is given as: Relative distances of two gases The relative distances traveled by the two gases is given as: Mathematically speaking, a gas with smaller molar mass will effuse faster than a gas with larger molar mass under the same condition.

## Connecting Gas Properties to Kinetic Theory of Gases

Molecular Diffusion Similar to effusion, the process of diffusion is the spread of gas molecules through space or through a second substance such as the atmosphere. The passage of one gas through another substance.

In this example, the other substance is another gas.