GATE PH concept:partition-function PYQs & Answers

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Questions 1–4 of 4. Imported answers require independent review unless marked reviewed.

Topic practice 4 questionsPage 1 of 1

The canonical partition function of an ideal gas is

where

and

denote temperature, volume, number of particles, and thermal de Broglie wavelength, respectively. Let

be the Boltzmann constant and

be the chemical potential. Take

. If the number density

at a temperature

, then

is ______

(rounded off to one decimal place).

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A simple harmonic oscillator with an angular frequency

is in thermal equilibrium with a reservoir at absolute temperature

, with

. Which one of the following is the partition function of the system?

Your answerChoose one option.

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A system of two atoms can be in three quantum states having energies

and

. The system is in equilibrium at temperature

. Match the following Statistics with the Partition function.

Statistics	Partition function
CD: Classical (distinguishable particles)	Z1:
CI: Classical (indistinguishable particles)	Z2:
FD: Fermi-Dirac	Z3:
BE: Bose-Einstein	Z4:

Your answerChoose one option.

CD: Z1, CI: Z2, FD: Z3, BE: Z4

CD: Z2, CI: Z3, FD: Z4, BE: Z1

CD: Z3, CI: Z4, FD: Z1, BE: Z2

CD: Z4, CI: Z1, FD: Z2, BE: Z3

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The partition function of an ensemble at a temperature

where

is the Boltzmann constant. The heat capacity of this ensemble at

, where the value of X is ______ (up to one decimal place).

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GATE PH concept:partition-function PYQs

How to practice concept:partition-function

Question 59

Question 38

Question 37

Question 53