# Entropy of a classical ideal gas using the concept of microcanonical ensemble

The microcanonical ensemble describes a system that is isolated and has a fixed total energy. For an ideal gas, the total energy of the system is the sum of the kinetic energies of all its constituent particles.

Consider a microcanonical ensemble for a system of 'N' non interacting point particles of mass M confined in a volume 'V' with total energy △E and E.

The volume of microcanonical ensemble in phase space is given by

where momentum space integral is to be evaluated subjected to constraint,

The range △E can be replaced by the range 0 to E. So,

S(E, V) = KBlog Γ (E) can be expressed as

S(E, V) = KBlog Σ (E) ..................3

Σ (E) is dimensionless so we introduce a constant having dimension of momentum X distance

This is the required expression for entropy of a classical ideal gas.

This note is taken from Statistical Mechanics, MSC physics, Nepal.

This note is a part of the Physics Repository.

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