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​For a micro-canonical system, the correct probability distribution function for energy is given by
Question

​For a micro-canonical system, the correct probability distribution function for energy is given by

A.

Exponential distribution function

B.

Gaussian distribution function

C.

Poisson distribution function

D.

Uniform distribution function

Correct option is D

Statistical thermodynamics uses molecular properties to predict the behavior of macroscopic quantities of different compounds.
An ensemble is assumed as an imaginary collection of a very large number of systems in different quantum states with common macroscopic properties such as pressure (P), Temperature (T), density, etc.
On the basis of the interaction of the number of ensembles with the surroundings, ensembles can be classified into four categories. These are
• Microcanonical ensemble,
• Canonical ensemble,
• Grand canonical ensemble, and
• Isobaric-isothermal ensemble
Microcanonical ensemble represents the possible states of a mechanical system whose total energy is specified. A microcanonical ensemble is a system that cannot exchange energy or particles with the surroundings. So, the energy of the system remains constant with time.
The macroscopic variables of the microcanonical ensemble that remains constant in the ensemble are the total number of particles in the system (N), the system's volume (V), as well as the total energy in the system (E). The microcanonical ensemble is sometimes called the NVE ensemble.
For a microcanonical system, since the macroscopic variables such as N, V, and E remains constant with time, the probability distribution function for energy will be a uniform distribution function.


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