Question
Unlike an ideal gas, a photon gas does not conserve this quantity; instead, this quantity scales with volume and temperature cubed. For 10 points each:
[10m] Name this quantity that is conserved in the microcanonical and canonical ensembles, but fluctuates in the grand canonical ensemble.
ANSWER: particle number [or N; or number of particles]
[10h] The product of the Riemann zeta function and this function appears in the expression for the particle number of a photon gas. The constant prefactor of the N-dimensional Maxwell–Boltzmann energy distribution can be written as “one over this function of N over two.”
ANSWER: gamma function [reject “gamma distribution”] (The Maxwell–Boltzmann distribution can be written as the gamma distribution.)
[10e] The product of the number density and energy density of a phonon gas reproduces the Stefan–Boltzmann law of these objects. These idealized objects absorb all light.
ANSWER: blackbodies [or blackbody]
<Physics>
Summary
| 2023 ACF Nationals | 04/22/2023 | Y | 20 | 16.00 | 100% | 50% | 10% |
Data
| Northwestern A | Claremont A | 10 | 0 | 10 | 20 |
| Cornell A | Imperial A | 10 | 0 | 10 | 20 |
| Yale B | WUSTL A | 10 | 0 | 10 | 20 |
| Iowa State A | Chicago B | 10 | 10 | 10 | 30 |
| Chicago C | MIT A | 10 | 0 | 10 | 20 |
| Columbia B | Purdue A | 0 | 0 | 10 | 10 |
| Florida A | South Carolina A | 0 | 0 | 10 | 10 |
| Georgia Tech B | NYU A | 0 | 0 | 10 | 10 |
| Johns Hopkins A | Virginia A | 0 | 0 | 10 | 10 |
| Chicago A | Minnesota A | 10 | 0 | 10 | 20 |
| Ohio State A | Texas A | 0 | 0 | 10 | 10 |
| Florida B | Penn State A | 0 | 0 | 10 | 10 |
| Harvard A | Rutgers A | 10 | 0 | 10 | 20 |
| Rutgers B | WUSTL B | 0 | 0 | 10 | 10 |
| Vanderbilt A | Houston A | 0 | 0 | 10 | 10 |
| Stanford A | Cornell B | 10 | 0 | 10 | 20 |
| Illinois A | Georgia Tech A | 0 | 10 | 10 | 20 |
| Duke A | Michigan A | 10 | 0 | 10 | 20 |
| Toronto A | Indiana A | 0 | 0 | 10 | 10 |
| UC Berkeley B | McGill A | 10 | 0 | 10 | 20 |