GATE PH 2021 Paper 1 — page 16

Questions 46–48 of 65. Imported answers require review unless explicitly marked reviewed.

Consider a single one-dimensional harmonic oscillator of angular frequency

, in equilibrium at temperature

. The states of the harmonic oscillator are all non-degenerate having energy

with equal probability, where

is the quantum number. The Helmholtz free energy of the oscillator is

Your answerChoose one option.

You can attempt this question now. Sign in to view the answer key, explanations and discussion.Log in to check answer

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

You can attempt this question now. Sign in to view the answer key, explanations and discussion.Log in to check answer

The free energy of a ferromagnet is given by

, where

, and

are positive constants,

is the magnetization,

is the temperature, and

is the Curie temperature. The relation between

and

is best depicted by

Your answerChoose one option.

You can attempt this question now. Sign in to view the answer key, explanations and discussion.Log in to check answer

2021 · Paper 1