JEE Main 2021 · 22 July · evening · Single correct · +4 / −1
What will be the average value of energy for a monoatomic gas in thermal equilibrium at temperature T?
- (a) 3/2k_BT
- (b) k_BT
- (c) 2/3k_BT
- (d) 1/2k_BT
Answer and solution
Answer (a) 3/2k_BT
Solution
Physics sir · 3 steps
A single atom can only move, not rotate or vibrate: three degrees of freedom, each worth half kT.
- Count degrees of freedom. A monoatomic gas molecule is a single point-like atom. It can move along x, y and z, so it has f = 3 translational degrees of freedom. Rotation about its own axis stores no energy, and there is no bond to vibrate.
- Equipartition. In thermal equilibrium, every degree of freedom carries an average energy of 1/2k_B T. The average energy per molecule is f/2k_B T.
Ē = 3 × 1/2k_B T = 3/2k_B T
- So. The average energy of a monoatomic gas molecule is 3/2k_B T, which is option (a).
The idea to keep. Average energy per molecule is f/2k_B T. Count f first: 3 for monoatomic, 5 for rigid diatomic, and add 2 for each vibrational mode.
Answer from the NTA final answer key. Solution by PrepWiser.