Discussion
A three-dimensional classical Harmonic Oscillator is in thermal equilibrium with a heat reservoir at temperature T. Its average total energy would be :
Answer: D
The average total energy is 3 \(k_{B}T\).
The energy of a three-dimensional classical oscillator has six quadratic terms: three kinetic, \(p_{x}^{2}/2m\) and so on, and three potential, \(\frac{1}{2}kx^{2}\) and so on. By the equipartition theorem each quadratic term contributes \(\frac{1}{2}k_{B}T\):
\[ \langle E \rangle = 6 \times \frac{1}{2}k_{B}T = 3k_{B}T \]
\(\frac{3}{2}k_{B}T\) is the kinetic energy alone, as for a free particle. \(k_{B}T\) is a one-dimensional oscillator, and 6 \(k_{B}T\) wrongly gives each quadratic term a full \(k_{B}T\).
Post your comment
Please log in or register to post a comment.
Examination Categories
- SSC Exams
- Banking Exams
- Teaching Exams
- Civil Services Exams
- Railways Exams
- Engineering Recruitment Exams
- Defence Exams
- State Government Exams
- Police Exams
- Insurance Exams
- Nursing Exams
- Other Government Exams
- NRA CET
- PG Entrance Exams
- Campus Placement
- MBA Entrance Exams
- CUET and UG Entrance
- Judiciary Exams
- Regulatory Body Exams
- Software Development