Rayleigh–Jeans law - 2025 ACF Regionals

Question

This law can be derived by using the equipartition theorem to determine the number of half-wave cycles that can fit within an arbitrary volume. For 10 points each:

[10h] Name this law that predicts a radio spectral index of 2 in the long-wavelength regime. This law can be used to approximate the brightness temperature as inversely proportional to the square of frequency.

ANSWER: Rayleigh–Jeans law

[10e] The “ultraviolet catastrophe” predicted by the Rayleigh–Jeans law was fixed by this law of blackbody radiation that also demonstrated that the energy emitted by a blackbody is quantized.

ANSWER: Planck’s law

[10m] The Rayleigh–Jeans law holds when the energy quantum is smaller than this expression. The equipartition theorem states that each degree of freedom contributes one-half of this expression.

ANSWER: kT [or k-sub-B T; or k times T; or k-sub-B times T; or the product of Boltzmann’s constant and temperature; accept one over thermodynamic beta; accept inverse of thermodynamic beta; reject “thermodynamic beta”]

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Summary


California	2025-02-01	Y	3	13.33	67%	33%	33%
Great Lakes	2025-02-01	Y	5	4.00	40%	0%	0%
Lower Mid-Atlantic	2025-02-01	Y	6	5.00	33%	17%	0%
Midwest	2025-02-01	Y	6	15.00	50%	50%	50%
North	2025-02-01	Y	3	10.00	67%	33%	0%
Overflow	2025-02-01	Y	5	16.00	80%	60%	20%
Pacific Northwest	2025-02-01	Y	2	10.00	50%	0%	50%
South Central	2025-02-01	Y	2	20.00	100%	100%	0%
Southeast	2025-02-01	Y	4	10.00	50%	25%	25%
UK	2025-02-01	Y	10	15.00	70%	60%	20%
Upper Mid-Atlantic	2025-02-01	Y	8	10.00	50%	38%	13%
Upstate NY	2025-02-01	Y	3	3.33	33%	0%	0%

Data


UCLA	Claremont A	0	10	0	10
UC Berkeley A	Claremont B	0	10	10	20
UC Berkeley B	UCSD	10	0	0	10
Carleton	Wisconsin A	0	0	0	0
Iowa State	Winona State	0	10	10	20
Wisconsin B	Minnesota B	0	10	0	10
Cambridge A	Oxford B	10	10	10	30
Cambridge E	Cambridge C	0	10	0	10
Cambridge B	Cambridge D	0	10	10	20
Durham	Imperial A	0	0	0	0
LSE	Imperial B	0	10	10	20
Warwick A	Manchester	0	10	0	10
Carnegie Mellon A	Ohio State A	0	10	0	10
Carnegie Mellon B	Michigan D	0	0	0	0
Case Western B	Case Western A	0	0	0	0
Michigan A	Michigan State	0	10	0	10
Kenyon	Ohio State B	0	0	0	0
William & Mary	Duke	0	0	0	0
Stanford B	Georgetown A	10	0	0	10
Northwestern A	Georgetown B	0	10	10	20
Iowa	Notre Dame B	0	10	0	10
Northwestern B	Purdue	0	10	10	20
Notre Dame A	Notre Dame C	0	10	10	20
UW A	Alberta	10	10	0	20
UBC	UW B	0	0	0	0
Texas A	TAMU	0	10	10	20
ASU	Texas B	0	10	10	20
Oxford A	Warwick B	0	10	10	20
Oxford C	Southampton A	10	0	10	20
Bristol	Sheffield	0	10	10	20
NYU C	Southampton B	0	0	0	0
ESF A	Cornell D	0	0	0	0
RIT A	Cornell C	0	10	0	10
Binghamton A	RIT B	0	0	0	0
UNC B	Liberty A	0	10	10	20
Liberty C	UNC D	0	0	0	0
Virginia Tech A	South Carolina	0	10	0	10
Liberty B	UNC C	0	0	0	0
Virginia A	Wake Forest	0	0	0	0
Chicago A	Chicago B	10	10	10	30
Missouri S&T	Chicago D	0	0	0	0
Illinois B	Indiana B	0	0	0	0
WashU A	Illinois C	0	0	10	10
Indiana A	Illinois A	10	10	0	20
Chicago C	Missouri	10	10	10	30
Georgia Tech C	Alabama A	0	0	0	0
Vanderbilt A	Louisville A	0	0	0	0
Georgia Tech D	Tennessee A	0	10	0	10
Bruin A	Georgia Tech B	10	10	10	30
Columbia B	Haverford B	0	0	10	10
Columbia C	Cornell B	0	0	0	0
John Jay College	NYU A	0	10	10	20
Rutgers A	Johns Hopkins A	0	10	0	10
Penn B	Maryland B	0	0	0	0
NYU B	George Washington A	0	10	0	10
Penn A	George Washington B	10	10	10	30
Vassar A	Yale A	0	0	0	0