Introduction video
Video with 35 minute derivation of the multiplicity of an ideal gas.
1 A Quantum Mechanical ideal gas consists of N particles in a box (infinite square well) of edge length L. The system is thermally isolated, so no heat allowed in or out. I slowly increase the box size L. What happens to the total energy U of the system?
A) U increases B) U decreases C) U remains constant
2 The microstates of a 3D particle in a box are represented by points in “n-space”. How many microstates are there in a 5x4x3 volume of phase space?
A) Impossible to tell without more information B) 5x4x3=60 C) Some integer (>1) multiple of 60 D) 512 E) 5(4+3) = 57
3 Consider a QM ideal monatomic gas with N atoms, total energy U, in volume V. If the mass m of the particles is increased, keeping N, U, and V fixed, does the multiplicity change?
A) Yes, the multiplicity increases B) Yes, the multiplicity decreases C) No, there is no change in multiplicity.
- Weakly coupled ideal gases.
- Generalization:
- Equilibrium conditions
- (micro) multiplicity => (macro) entropy
4 Free expansion of a gas. A gas is confined to the left half of a thermally-isolated container. Suddenly, the partition breaks and the gas fills the whole container.
The internal energy U of the gas
A) increases B) decreases C) remains constant
5 Did the entropy of the gas change?
A) yes, entropy increased B) Yes, entropy decreased C) No, there was no change in entropy