Statistical Physics MCQ Level – 2 - IIT JAM MCQ

Average energy of a system is defined as


The correct answer is: 

The Fermi energy is given by

The correct answer is: N^2/3

In a semi-classical derivation of entropy that does not take into account the indistinguishability of particles, yields an expression for the entropy which is not extensive. This is called Gibb’s Paradox.
The correct answer is: Distinguishability of classical particles

The particle density and temperature T are related as

The correct answer is:  

Let us take  where V is volume and N is number of particles.
Now, for 
i.e. when interparticle is much larger than the thermal de-Broglie wavelength, the gas will obey Maxwell Boltzmann Statistics.
The correct answer is: When de-Broglie wavelength is much smaller than the inter-particle distance

Let 
∴ 


∴ 
The correct answer is:  

Partition function 

⇒ 
The correct answer is: 

Partition function of single gas molecule = Z_α
Since N particles are non-interacting, the partition function = 

The correct answer is: 

Classical partition function Z gives nothing but sum of all the possible states. In discrete systems, it gives basically the sum over all the microstates and in continuous systems it is represented in terms of integrating.
The correct answer is: Sum of states of the system

The phase space volume is 
where  
and   is limited by 

Hence 
∴ Volume of phase space 

Number of phase space = 

The number of microstates in the energy range E to  is


The correct answer is: