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i want detailed explanation of kinetic theory of gases,thermodynamics

12 years ago

hi tarun,

kinetic theory of gas is

Gases can be studied by considering the small scale action of individual molecules or by considering the large scale action of the gas as a whole. We can directly measure, or sense, the large scale action of the gas. But to study the action of the molecules, we must use a theoretical model. The model, called the **kinetic theory of gases**, assumes that the molecules are very small relative to the distance between molecules. The molecules are in constant, random motion and frequently collide with each other and with the walls of any container.

The individual molecules possess the standard physical properties of mass, momentum, and energy. The density of a gas is simply the sum of the mass of the molecules divided by the volume which the gas occupies. The pressure of a gas is a measure of the linear momentum of the molecules. As the gas molecules collide with the walls of a container, the molecules impart momentum to the walls, producing a force that can be measured. The force divided by the area is defined to be the **pressure**. The temperature of a gas is a measure of the mean kinetic energy of the gas. The molecules are in constant random motion, and there is an **energy** (mass x square of the velocity) associated with that motion. The higher the temperature, the greater the motion.

In a solid, the location of the molecules relative to each other remains almost constant. But in a gas, the molecules can move around and interact with each other and with their surroundings in different ways. As mentioned above, there is always a **random** component of molecular motion. The entire fluid can be made to move as well in an ordered motion (flow). The ordered motion is superimposed, or added to, the normal random motion of the molecules. At the molecular level, there is no distinction between the random component and the ordered component. We measure the pressure produced by the random component as the **static pressure**. The pressure produced by the ordered motion is called dynamic pressure. And Bernoulli's equation tells us that the sum of the static and dynamic pressure is the **total pressure** which we can also measure.

kinetic theory of ideal gas makes following assumptions...:

The theory for ideal gases makes the following assumptions:

- The gas consists of very small particles, all with non-zero mass.
- The number of molecules is large such that statistical treatment can be applied.
- These molecules are in constant, random motion. The rapidly moving particles constantly collide with the walls of the container.
- The collisions of gas particles with the walls of the container holding them are perfectly elastic.
- The interactions among molecules are negligible. They exert no forces on one another except during collisions.
- The total volume of the individual gas molecules added up is negligible compared to the volume of the container. This is equivalent to stating that the average distance separating the gas particles is large compared to their size.
- The molecules are perfectly spherical in shape, and elastic in nature.
- The average kinetic energy of the gas particles depends only on the temperature of the system.
- 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 can be treated as classical objects.
- The time during collision of molecule with the container's wall is negligible as comparable to the time between successive collisions.
- The equations of motion of the molecules are time-reversible.

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. 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. In the other limit, for extremely rarefied gases, the gradients in bulk properties are not small compared to the mean free paths. 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.

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