Some elementary deductions from kinetic theory of gases

Some elementary deductions from kinetic theory of gases

From equation (9.12), we know that PV=2/3 U But the internal energy of an ideal gas is equal to N times the average kinetic energy (∈) of each molecule.

U = N∈

For a fixed temperature, the average translational kinetic energy ∈ will remain constant. It implies that

Therefore, pressure of a given gas is inversely proportional to its volume provided the temperature remains constant. This is Boyle’s law.

Charles’ law:

From the equation (9.12), we get PV = 2/3U

For a fixed pressure, the volume of the gas is proportional to internal energy of the gas or average kinetic energy of the gas and the average kinetic energy is directly proportional to absolute temperature. It implies that

V∝T or V/T = constant

This is Charles’ law.

Avogadro’s law:

This law states that at constant temperature and pressure, equal volumes of all gases contain the same number of molecules. For two different gases at the same temperature and pressure, according to kinetic theory of gases,

From equation (9.6)

are the mean square speed for two gases and N₁ and N₂ are the number of gas molecules in two different gases.

At the same temperature, average kinetic energy per molecule is the same for two gases.

Dividing the equation (9.15) by (9.16) we get N₁ = N₂

This is Avogadro’s law. It is sometimes referred to as Avogadro’s hypothesis or Avogadro’s Principle.