Statistical Physics MCQ Level – 1 - IIT JAM MCQ

In the equilibrium state, the system attains the most stable state and the only possibility of finding the system is that particular equilibrium state, hence the probability in that state is 1.
The correct answer is: one

According to probability theory,
Number of ways for choosing n atoms out of N atoms 
and number of ways for putting n atoms in N' site 
∴ Total number of microstates are

The correct answer is: 

Micro canonical ensemble, N, V and E are constants of the ensemble, hence MC : (E, V, N)
For canonical ensemble N, V and T are constants hence CE : (N, V, T)
For grand canonical ensemble, V, T and µ are constants hence GC : (V, T, µ)
The correct answer is: MC : (E, V, N); CE : (N, V, T); GC : (V, T, µ)

It is about conservation of density of point  in phase space.
∴ 
or 
Using Hamiltonian’s equation of motion

and  
We get 

[ρ,H] represents poisson’s bracket.
The correct answer is: 

In a microcanonical ensemble, the system is assumed to be isolated in the sense that the system cannot exchange energy or particles with its environment, so that the energy of the system remains exactly known as the time goes on.
The correct answer is: A can exchange neither energy nor particles with B

A canonical ensemble is the statistical ensemble that represents the possible states of a mechanical system in thermal equilibrium with a heat bath at a fixed temperature.
The correct answer is: Thermal equilibrium of system

For the particle, volume of phase space corresponding to one microstate is
dV = (dxdydz)(dp_xdp_ydp_z)
= h³
For N interacting particles, the volume of one microstate is

= (h³)·h³ ···N terms

The correct answer is: h^3N

Probability is given by

Here m = 0

The correct answer is:  

In canonical ensemble, system can exchange energy with the heat bath so that the states of the system will differ in total energy.
The correct answer is: A can exchange only energy with B

Since, we take energy interval where phase density remains constant, and energy is the constant of the ensemble, we tend to consider the phase density to be zero outside thus interval.
The correct answer is: Zero