Atoms, which are tiny particles constantly in motion, are the basic building blocks of everything. The atomic hypothesis suggests that all matter is made of atoms that are in constant motion and can move freely. They attract and repel each other when forced to be close to each other.

The atomic theory was proposed by John Dalton; it explains how elements combine to form compounds and how they obey laws of definite and multiple proportions. He is credited with developing 'Atomic Theory,' a scientific theory. According to the first law, the constituents of each compound have a fixed mass proportion. The second law states that when two elements combine to form more than one compound,  the masses of the other elements are in a ratio of small integers for a fixed mass of one element.

Atoms of an element are made of the same particles and combine to form molecules. These differ from other elements. Gay Lussac’s law suggests that when gases combine to form another gas, their volumes are in the ratio of small integers. Avogadro’s law explains that under the same amount of pressure and temperature, all gases have an equal number of particles. Gaylusaac’s law is explained using a combination of atomic theory and Avogadro’s law. The molecular theory is the gist of Dalton’s theory. The distance that the particles can travel without collision is the mean free path. When the atoms are at a distance, then they attract each other, and they repel when they are close enough. 

Atomic theory by dalton considers atoms as indivisible, but now the inner nuclear particles are found out. Quarks make the nucleons, and there may be particles that make up the quarks. The quest continues.

Because molecules in a gas are so far apart, mutual interactions are minimal unless two molecules collide. The properties of gases are simpler to understand than those of solids and liquids. Gases at reduced pressure and much increased temperature than those at which they liquefy (or solidify) approximate a simple relationship between pressure, temperature, and volume given by a given sample of the gas. Avogadro's theory states that the number of molecules per unit volume is the same for all gases at a fixed temperature and pressure.

Gases are in continuous motion. The average distance between the molecules is in the molecular range. So, the interatomic interaction could be considered small, and the particles are approximated to move in a straight line. When they come in the range of another particle, interatomic forces take control, and their velocities vary. This is called a collision. They are elastic in nature, where total kinetic energy and momentum are conserved.
Elastic collision of gases can be approximated to take place in a rectangular box. From the total momentum of the particles, the root-mean-square velocity of the atoms can be extracted. This leads to the expression for pressure,

Where \( \overline \upsilon ~2 \)2 is the sum of squares of velocities in the x, y, z-direction

M: mass of the particles

N: number density of particles

P: the pressure of the particles

The average kinetic energy of the gas is proportional to the absolute temperature and independent of other macroscopic properties like pressure, volume, etc. Using the Boltzmann constant, this is found to be

E/N: Average kinetic energy

k_B: Boltzmann constant

T: Temperature

The translational kinetic energy of the system is E=3/2 N k_BT

And from this, the pressure could be found out as,

P: Pressure

V: Volume

If a system is in thermal equilibrium, at absolute temperature, the total energy is distributed in the different modes equal k_BT. The modes represent the degrees of freedom for the molecule. That is, the particles exhibit rotational and vibrational energy. Depending on the degrees of freedom, the energy is distributed in each mode. That is, if the system has one vibrational mode, energy is KBT. If it has two modes, then energy is 2K_BT and soon. This law can be used to determine the specific heat capacities of gases, and these do obey the real values. The addition of kinetic and potential vibrational energy also improves this approximation.

The temperature of a body could be measured by us. When heat is absorbed or liberated there, is a change in energy. The change in temperature of a body when heat is absorbed or released is the concept behind heat capacity. The amount of heat required to raise the temperature of a unit mass of a substance by a unit degree Celsius is termed specific heat capacity.  If measured in moles, it is called molar-specific heat.

The following expression will be required for solving problems:

Where:

S : Specific heat capacity of the substance

\( \Delta \) Q : Change in heat energy

\( \Delta \) T : Change in temperature

If specific heat capacity is obtained under constant pressure, it is Cp. If it is under constant volume is Cv. Both are different for the same materials. According to the Dulong–Petit law and law of equipartition, the specific heat at the constant volume of a solid is 3R.

The mean free path is the average length of a molecule's free path. The mean free path is the average distance a molecule can travel without colliding. Interatomic distances in gases are measured in tens of angstroms.   In gases, the mean free path is measured in thousands of angstroms. In dynamic equilibrium, molecules collide and their speeds change as a result of the collision.   In gases, atoms are far freer and can travel long distances without colliding. Gases escape if they are not enclosed. The interatomic force is important in solids and liquids due to their proximity. By a few angstroms, the atoms attract each other but repel each other as they get closer.

Where l: the average distance covered by particles in between successive collisions

n: number density 

D: diameter of the molecule

1. What is the Kinetic Theory of Gases?

A. The kinetic theory of gases is a simple theory which is aimed to solve the properties of gases. It approximates that all particles in a gaseous system consist of small atoms, and the interatomic interactions are neglected. It also uses the Boltzmann concept and distribution of energy in the various modes. The theory also suggests that temperature is the only property that the kinetic energy of a gas depends on. It is independent of the nature of the gases or other macroscopic properties.

2. What is Stated in Charles' Law?

A. If in a system the pressure is kept constant, Charles law states that the volume of the gas is directly proportional to its absolute temperature.  As temperature increases, the volume of the gas also increases. For example, consider a balloon filled with gas. If it is placed in direct sunlight, after some time, the balloon bursts. 

V= kT

Where V: volume of the gas

K: Constant of proportionality

T: Temperature of the gas

3. What do the Postulates of Kinetic Theory State?

A. The main postulates of the kinetic theory are

1. Gases are made up of small independent atoms. Atoms of the same element are alike.

2. These molecules are in random motion with a certain velocity.

3. If the gases are taken inside a conductor, these particles will collide with the walls of the container elastically.

4. These collisions are elastic in nature, and energy and momentum are conserved.

5. Molecules do not exert force on each other.

6. Volume of the gases is small compared to the volume of gases.

7. The total kinetic energy of a system only depends on the temperature of the system.

4. What is the Mean free path?

A. Mean free path is the average distance that molecules in a gas can travel in between collisions. Or it can be defined as the distance between two successive collisions. It depends on the number, density, and diameter of the molecules.