A system of N non-interacting classical particles, each of mass m is in a two dimensional harmonic potential of the form V(r)=\alpha \left( {x}^{2}+{y}^{2} \right) where \alpha is a positive constant. The canonical partition function of the system at temperature T is \left( \beta =\frac{1}{{k}_{B}T} \right):

Canonical Ensemble — CSIR Net PYQ (Question 4)

A Canonical Ensemble previous-year question (PYQ) from Statistical Mechanics (CSIR Net). Read the question, check the correct answer, then practise the full topic.

Question 4 of 36 · 3.5 marks

A system of

N

non-interacting classical particles, each of mass

m

is in a two dimensional harmonic potential of the form

V (r) = α (x^{2} + y^{2})

where

α

is a positive constant. The canonical partition function of the system at temperature

T

(β = \frac{1}{k _{B} T})

1 $[(\frac{α}{2 m})^{2} \frac{π}{β}]^{N}$
2 $(\frac{2 mπ}{α β})^{2 N}$
3 $(\frac{α π}{2 m β})^{N}$
4 $(\frac{2 m π ^{2}}{α β ^{2}})^{N}$

Correct answer: Option 4

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This Canonical Ensemble PYQ is part of the Statistical Mechanics section of CSIR Net. Browse more Canonical Ensemble questions or join the PhysicsByAaryan live batch for full conceptual coverage.