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Assumptions in kinetic theory of gases
Assumptions of Kinetic Theory of Gases:
All gases are made of molecules moving randomly in all directions.
The size of a molecules is much smaller than the average separation between the molecules.
The molecules exert no force on each other or on the walls of the container except during collision.
All collisions between two molecules or between a molecule and a wall are perfectly elastic. Also, the time spent during a collision is negligibly small.
The molecules obey Newton's laws of motion.
When a large number of molecules of a gas is left for sufficient time, it comes to a steady state. The densities and distribution of the molecules with different velocities are independent of position, direction and time.
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Ideal gas equation
The ideal gas equation is
Assumptions:
(1) the gas consists of a large number of molecules, which are in random motion and obey Newton's laws of motion; (2) the volume of the molecules is negligibly small compared to the volume occupied by the gas; and (3) no forces act on the molecules except during elastic collisions of negligible duration.
Assumptions:
(1) the gas consists of a large number of molecules, which are in random motion and obey Newton's laws of motion; (2) the volume of the molecules is negligibly small compared to the volume occupied by the gas; and (3) no forces act on the molecules except during elastic collisions of negligible duration.
Boyle's Law
The absolute pressure exerted by a given mass of an ideal gas is inversely proportional to the volume it occupies if the temperature and amount of gas remain unchanged within a closed system.
Charle's law
When the pressure on a sample of a dry gas is held constant, the Kelvin temperature and the volume will be directly related.
Average pressure in terms of root mean square speed.
where, no. of molecules
=molecular mass
=average r.m.s velocity
kinetic interpretation of temperature
The translational kinetic energy is
where is the number of molecules
where is the number of molecules
Law of equipartition of energy
The law of equipartition of energy states that if a system is in equilibrium at absolute temperature , the total energy is distributed equally in different energy modes of absorption, the energy in each mode being equal to . Each translational and rotational degree of freedom corresponds to one energy mode of absorption and has energy . Each vibrational frequency has two modes of energy (kinetic and potential) with corresponding energy equal to
Root mean square velocity variation with temperature and molecular weight
Mean free path
The mean free path is the average distance a molecule can travel without colliding, after which its direction or energy gets modified.
where is the mean free path, is the number density(number of molecules per unit volume) and is the diameter of the molecule.
where is the mean free path, is the number density(number of molecules per unit volume) and is the diameter of the molecule.
