IGNOU BPHCT 135 2026 - Derive an expression of the partition function for a single particle m

Question

Derive an expression of the partition function for a single particle monatomic ideal gas. Write the expression for a monatomic gas consisting of N-identical yet distinguishable and non-interacting particles.

19 Jan 2026

Answer :

Word Count : 262

For a single particle of a monatomic ideal gas, the partition function is derived from the principles of statistical mechanics. A monatomic particle has only translational degrees of freedom, and its energy is purely kinetic. The energy of a particle in three dimensions is given by ( \varepsilon = \frac{p_x^2}{2m} + \frac{p_y^2}{2m} + \frac{p_z^2}{2m} ), where ( p_x, p_y, p_z ) are the momentum components and ( m ) is the particle mass. The single-particle canonical partition function ( Z_1 ) is defined as the sum over all possible states, weighted by the Boltzmann factor ( e^{-\varepsilon / k_B T} ). For continuous translational states,

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