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NEET Physics Notes Mechanics-Behaviour of Perfect Gas and Kinetic-Law of Equipartition of Energy

NEET Physics Notes Mechanics-Behaviour of Perfect Gas and Kinetic-Law of Equipartition of Energy

Law of Equipartition of Energy

Law of Equipartition of Energy

According to law of equipartition of energy for any system in thermal equilibrium, the total energy is equally distributed among its various degree of freedom and each degree of freedom is associated with energy
NEET Physics Notes Mechanics-Behaviour of Perfect Gas and Kinetic-Law of Equipartition of Energy 1(where, k = 1.38 x 10~23 J/K.
T = absolute temperature of the system).

Specific Heat Capacities of Gases

The specific heat of gas can have many values, but out of them following two values are important

Specific Heat at Constant Volume

The specific heat of a gas at constant volume is defined as the quantity of heat required to raise the temperature of unit mass of gas through 1°C or 1 K when its volume is kept constant i.e.
NEET Physics Notes Mechanics-Behaviour of Perfect Gas and Kinetic-Law of Equipartition of Energy 2
Specific Heat at Constant Pressure

The specific heat of a gas at constant pressure is defined as the quantity of heat required to raise the temperature of unit mass of gas through IK, when its pressure is
kept constant
NEET Physics Notes Mechanics-Behaviour of Perfect Gas and Kinetic-Law of Equipartition of Energy 3
NEET Physics Notes Mechanics-Behaviour of Perfect Gas and Kinetic-Law of Equipartition of Energy 4
Specific heat of a gas at constant pressure is greater than the specific heat at constant volume i.e. Cp >CV.
Cp and CV are related to each other according to relation,
NEET Physics Notes Mechanics-Behaviour of Perfect Gas and Kinetic-Law of Equipartition of Energy 5
Eq. (ii) is called Mayer’s relation.
If Cp and CV are measured in the units of work and R is also in the units of work (or energy), then Eq. (ii) becomesCp -Cv =R..

Specific Heat in Terms of Degree of Freedom

For a gas at temperature T, the internal energy
NEET Physics Notes Mechanics-Behaviour of Perfect Gas and Kinetic-Law of Equipartition of Energy 6
NEET Physics Notes Mechanics-Behaviour of Perfect Gas and Kinetic-Law of Equipartition of Energy 7

Mean Free Path

Every gas consists of a very large number of molecules. These molecules are in a state of continuous rapid and random motion. They undergo perfect elastic collisions against one another. Therefore, path of a single gas molecule consists of a series of short zig-zag paths of different lengths.
NEET Physics Notes Mechanics-Behaviour of Perfect Gas and Kinetic-Law of Equipartition of Energy 8
The mean free path of a gas molecule is the average distance between two successive collisions.
NEET Physics Notes Mechanics-Behaviour of Perfect Gas and Kinetic-Law of Equipartition of Energy 9
Here, α= diameter of the molecule and n = number of molecules per unit volume.

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