kinetic theory of gases

The kinetic theory of gases reveals the microscopic nature of macroscopic thermal phenomena and laws of gases by finding the relationship between macroscopic quantities and microscopic quantities. From the perspective of molecular motion, statistical methods are used to study the macroscopic properties and change patterns of thermal motion of gas molecules.

Edited at 2024-05-06 14:57:52

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kinetic theory of gases

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Outline

kinetic theory of gases

Basic concepts of molecular motion

Macroscopic objects are composed of a large number of particles (molecules, atoms, etc.). The molecules in the object are constantly undergoing disordered thermal motion.

Avogadro's number

There are interactions between molecules

The subtle nature of temperature

A sign of the intensity of thermal motion of molecules inside an object

equipartition theorem of energy

For an ideal gas with coverage D in equilibrium, the average kinetic energy of each degree of freedom of the molecule is equal and equal to kT/2

The average auxiliary energy of a molecule with i degrees of freedom is ikT/2

internal energy of ideal gas

The internal energy of an ideal gas is the sum of all forms of kinetic energy of all molecules and the potential energy between atoms within the molecules. For a given ideal gas, its internal energy depends only on temperature.

If vibration energy is not considered, the internal energy of an ideal gas with mass m is

ideal gas pressure formula

The pressure of a gas is caused by a large number of molecules constantly exerting force on the wall when they collide with the wall. It is a statistical average quantity.

Maxwell's law of rate distribution

Rate distribution function of molecules of an ideal gas in equilibrium

Ratio of the number of molecules distributed over a rate interval

Three statistical averages of molecular speed

average rate

square root rate

most probable rate

Boltzmann distribution rate

Molecules in a potential field always preferentially occupy states with lower potential energy.

The pressure of gas in the gravity field decreases exponentially with height

mean free path

The average distance a molecule moves between two consecutive collisions is called the mean free path

The principle of entropy increase

Boltzmann's principle

Ω is the total microstate number of the system

All processes that occur in an isolated system that is not affected by external energy proceed from a macro state with a small probability (a small number of micro states) to a macro state with a high probability (a large number of micro states).

The entropy of an isolated system never decreases