Packet 8: Bonus 12
Volume, temperature, and this quantity are held constant in the canonical ensemble. For 10 points each,
[10m] Name this quantity, which in a reformulation of the ideal gas law, equals P V over k T.
ANSWER: particle number [accept N; prompt on partial answer]
[10e] The BBGKY hierarchy couples the density function named for this quantity for n and n+1 particles. This quantity between zero and one gives the chance of observing a particle in a given state.
ANSWER: probability [accept probability density function; prompt on distribution function]
[10h] Finding the probability that a particle occupies a particular energy state in the Boltzmann distribution requires finding its Boltzmann factor and then dividing it by this function that normalizes the distribution.
ANSWER: partition function [accept canonical partition function or grand partition function; prompt on Z]
<Science - Physics, Rohan Ganeshan> | VAULT II Packet 08
| Heard | PPB | E % | M % | H % |
|---|---|---|---|---|
| 43 | 13.49 | 65% | 42% | 28% |
Conversion
Summary
| Tournament | Edition | Match | Heard | PPB | E % | M % | H % |
|---|---|---|---|---|---|---|---|
| VAULT II at Georgia Tech | 2026-01-24 | ✓ | 6 | 16.67 | 50% | 67% | 50% |
| Triangle Cup | 2026-03-13 | ✓ | 3 | 13.33 | 67% | 33% | 33% |
| VAULT II at Eden Prairie HS | 2026-03-13 | ✓ | 3 | 6.67 | 67% | 0% | 0% |
| VAULT II at McGill | 2026-03-13 | ✓ | 4 | 2.50 | 25% | 0% | 0% |
| VAULT II at UCSB | 2026-03-13 | ✓ | 4 | 25.00 | 100% | 100% | 50% |
| VAULT II Northern UK | 2026-04-24 | ✓ | 3 | 13.33 | 100% | 0% | 33% |
| VAULT II Southern UK | 2026-04-24 | ✓ | 4 | 10.00 | 50% | 50% | 0% |
| VAULT II at Harvard | 2026-04-30 | ✓ | 3 | 16.67 | 100% | 33% | 33% |
| VAULT II at MINT | 2026-06-19 | ✓ | 5 | 6.00 | 60% | 0% | 0% |
| VAULT II Stanford Online | 2026-07-17 | ✓ | 8 | 18.75 | 63% | 75% | 50% |