Question
The grand potential equals negative k T times the log of one form of this quantity. For 10 points each:
[10h] Name this quantity that is denoted “Z,” from the German for “sum over states,” because it is computed by summing over all microstates. Dividing weights by this quantity normalizes a Boltzmann distribution.
ANSWER: partition function [accept canonical partition function or grand canonical partition function; accept Zust·and·ssumme]
[10e] The grand canonical partition function is a sum of values for this scientist’s namesake “factor.” This scientist’s free energy equals H minus T S and determines spontaneity.
ANSWER: Josiah Willard Gibbs [accept Gibbs factor; accept Gibbs free energy]
[10m] The Gibbs factor over the grand partition function gives this quantity for a microstate. The wave function times its complex conjugate gives this quantity’s density.
ANSWER: probability [accept probability density or likelihood]
<Forrest Weintraub, Science - Physics> ~22929~ <Editor: David Bass>
Data
| Team | Opponent | Part 1 | Part 2 | Part 3 | Total |
|---|---|---|---|---|---|
| Barrington | Richard Montgomery A | 0 | 10 | 10 | 20 |
| Beavercreek | Downingtown STEM | 0 | 10 | 10 | 20 |
| Carl Sandburg | Maggie Walker C | 0 | 10 | 0 | 10 |
| Detroit Catholic Central A | Great Valley | 0 | 10 | 0 | 10 |
| Detroit Catholic Central B | Lindbergh | 0 | 10 | 0 | 10 |
| Detroit Catholic Central C | Solon | 0 | 10 | 0 | 10 |
| Georgetown Day | Canyon Crest | 0 | 10 | 10 | 20 |
| Hastings | University Lab | 0 | 10 | 0 | 10 |
| Heights | Hoover A | 0 | 10 | 10 | 20 |
| Hunter B | Winston Churchill B | 0 | 10 | 10 | 20 |
| Kinkaid | Innovation Academy A | 10 | 10 | 10 | 30 |
| Lambert | Belmont | 0 | 10 | 0 | 10 |
| Livingston A | Hunter A | 0 | 10 | 0 | 10 |
| Livingston B | Strake Jesuit | 0 | 10 | 10 | 20 |
| Maggie Walker A | Johns Creek B | 0 | 10 | 10 | 20 |
| McLean B | Thomas Jefferson B | 0 | 10 | 0 | 10 |
| Mexico | Lightridge | 0 | 10 | 0 | 10 |
| Northmont B | Thomas Jefferson C | 0 | 10 | 10 | 20 |
| Owensboro | Fairfield County AT | 0 | 10 | 0 | 10 |
| Richard Montgomery B | McLean A | 0 | 10 | 0 | 10 |
| Seven Lakes | Alabama Cyber Tech | 0 | 10 | 0 | 10 |
| St. Mark's | Johns Creek A | 0 | 10 | 10 | 20 |
| Stevenson A | Carbondale | 0 | 10 | 0 | 10 |
| Thomas Jefferson A | Winston Churchill A | 0 | 10 | 10 | 20 |
| Thomas Jefferson D | Northmont A | 0 | 10 | 0 | 10 |
| Walter Payton A | William Fremd | 0 | 10 | 10 | 20 |
Summary
| Tournament | Edition | Exact Match? | Heard | PPB | Easy % | Medium % | Hard % |
|---|---|---|---|---|---|---|---|
| 2024 PACE NSC | 06/08/2024 | Y | 26 | 15.00 | 100% | 46% | 4% |