Ludwig Boltzmann - 2025 ACF Winter

Question

Answer the following about the structure of the partition function of the canonical ensemble, for 10 points each.

[10e] In the discrete case, the partition function is a sum of expressions of this man’s namesake “factors.” This Austrian’s namesake constant is symbolized k-sub-B.

ANSWER: Ludwig Boltzmann [accept Boltzmann’s constant]

[10m] In the continuous case with indistinguishable particles, a factor of one over N-factorial appears so that this quantity is extensive. That factor properly accounts for this quantity’s “mixing” type in identical gases.

ANSWER: entropy [accept mixing entropy; prompt on S]

[10h] The continuous expression also includes a factor of one over h to the 3N, where h is Planck’s constant, so the partition function has this property. This property means that the partition function is invariant under rescaling.

ANSWER: dimensionless [or unitless; accept descriptions of having no units]

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Summary


California	Main	Y	5	20.00	100%	100%	0%
Canada	Main	Y	5	10.00	60%	40%	0%
Florida	Main	Y	13	10.77	85%	23%	0%
Great Lakes	Main	Y	6	8.33	50%	17%	17%
Lower Mid-Atlantic	Main	Y	7	11.43	71%	43%	0%
Midwest	Main	Y	10	9.00	70%	20%	0%
North	Main	Y	11	9.09	55%	36%	0%
Northeast	Main	Y	5	10.00	80%	20%	0%
Overflow	Main	Y	4	15.00	100%	50%	0%
Pacific Northwest	Main	Y	12	11.67	92%	25%	0%
South Central	Main	Y	2	10.00	100%	0%	0%
Southeast	Main	Y	11	13.64	91%	46%	0%
UK	Main	Y	4	15.00	100%	50%	0%
Upstate NY	Main	Y	8	11.25	88%	25%	0%
2025 ACF Nationals	2025-08-09	Y	10	12.00	100%	20%	0%
2024 ARCADIA at UC Berkeley	04/19/2025	Y	3	6.67	67%	0%	0%
2024 ARCADIA at UC Berkeley	04/19/2025	Y	1	20.00	100%	100%	0%

Data


Berkeley A	Berkeley B	10	10	0	20
Berkeley D	Berkeley C	10	10	0	20
Berkeley E	Berkeley F	10	10	0	20
Stanford A	Stanford B	10	10	0	20
UCSD Two Running Violet V Forms	USC	10	10	0	20
Stanford C	UCSC	10	10	0	20
UCLA A	UCI	10	0	0	10
UCLA B	UCSD What Hath God Wrought	10	0	0	10
UCLA C	UCLA D	0	10	0	10
Claremont Pitzer	UCSB	0	0	0	0
Carleton	McMaster C	10	0	0	10
Toronto C	Guelph A	10	0	0	10
McMaster A	McGill A	10	0	0	10
Toronto K	McGill C	0	0	0	0
Western Ontario	McMaster B	10	0	0	10
Queen's B	Waterloo	10	0	0	10
Toronto A	Ottawa	10	10	0	20
Toronto B	Toronto D	10	10	0	20
Toronto E	Guelph B	10	10	0	20
Toronto Metropolitan	Toronto F	0	0	0	0
Queen's A	Toronto H	10	0	0	10
Toronto I	McGill B	10	0	0	10
Toronto G	Toronto J	10	0	0	10
FIU	UF C	0	0	0	0
UF E	FSU	0	0	0	0
UCF A	Melbourne B	10	0	0	10
UCF B	USF	10	0	0	10
UF B	UF D	0	0	0	0
CWRU A	OSU D	10	10	0	20
Kenyon B	CWRU C	0	0	0	0
CWRU D	Kenyon A	10	0	0	10
Pitt B	MSU B	10	10	0	20
Pitt A	OSU A	10	0	0	10
OSU B	MSU A	0	0	0	0
OSU C	CWRU B	10	10	0	20
UF A	Melbourne A	10	10	10	30
Virginia B	Clemson A	10	0	0	10
Tusculum	Clemson B	10	10	0	20
James Madison	Liberty A	0	0	0	0
South Carolina B	NC State	0	0	0	0
North Carolina A	Liberty B	10	10	0	20
North Carolina B	North Carolina C	10	0	0	10
South Carolina A	Virginia Tech B	10	0	0	10
Tennessee A	Virginia A	10	0	0	10
Roanoke	Tennessee B	0	0	0	0
George Mason A	Maryland D	0	0	0	0
Penn A	George Mason B	10	10	0	20
George Mason C	Penn B	0	0	0	0
Georgetown B	Catholic University	10	0	0	10
George Washington B	Johns Hopkins B	0	10	0	10
Georgetown A	Maryland A	0	0	0	0
Maryland B	Johns Hopkins C	10	10	0	20
NYU A	Johns Hopkins A	10	0	0	10
UMBC A	NYU B	0	0	0	0
Notre Dame E	George Washington A	10	0	0	10
Maryland C	VCU A	10	10	0	20
Virginia Tech A	Liberty C	10	0	0	10
Columbia A	Lehigh A	10	0	0	10
Princeton A	Columbia B	10	0	0	10
Columbia C	Lehigh B	10	10	0	20
Swarthmore A	Rutgers C	10	0	0	10
Rowan A	Vassar A	0	0	0	0
Michigan B	Chicago A	10	0	0	10
Purdue A	Chicago B	10	10	0	20
Kentucky	Chicago C	10	10	0	20
Notre Dame C	Chicago D	10	0	0	10
Illinois C	Indiana A	10	0	0	10
Illinois A	Michigan A	10	0	0	10
Louisville A	Michigan C	10	10	0	20
Indiana B	Michigan D	0	0	0	0
Illinois B	Notre Dame B	10	0	0	10
Notre Dame D	Purdue C	10	0	0	10
Louisville B	Purdue B	10	0	0	10
Notre Dame A	UIC	10	0	0	10
Missouri B	Truman State	10	0	0	10
WashU A	William Woods	10	10	0	20
Missouri A	WashU B	10	10	0	20
WashU C	SIUE	10	0	0	10
Macalester B	Iowa State	10	0	0	10
Minnesota A	Carleton	10	0	0	10
Brown B	Amherst B	10	0	0	10
BC A	Brandeis Orlando	0	0	0	0
BC B	Brandeis Wilson	10	10	0	20
BU	Brown A	10	10	0	20
MIT A	Brandeis Clemenceau	10	10	0	20
Harvard	Brown C	10	0	0	10
Amherst A	MIT B	10	10	0	20
Tufts A	Bowdoin B	10	10	0	20
Tufts B	Brandeis Lloyd George	10	0	0	10
Williams	Dartmouth	10	0	0	10
Yale A	Cornell-UG	10	0	0	10
British Columbia D	British Columbia A	10	10	0	20
British Columbia C	British Columbia B	10	0	0	10
Washington A	Simon Fraser	10	0	0	10
Washington B	Alberta	10	10	0	20
Auburn A	Vanderbilt A	10	10	0	20
Bruin A	Alabama A	10	0	0	10
Huntsville A	Georgia Tech C	10	0	0	10
Alabama B	Mississippi State A	10	0	0	10
Georgia Tech B	Sewanee A	10	0	0	10
Huntsville B	UAB A	10	0	0	10
Vanderbilt B	Auburn B	0	0	0	0
Cambridge B	Birmingham A	10	0	0	10
Bristol B	LSE A	10	10	0	20
Edinburgh A	Cambridge C	10	0	0	10
Sheffield A	Cambridge D	10	0	0	10
Imperial A	City St George's A	10	0	0	10
Durham A	Southampton B	10	0	0	10
Manchester A	Imperial C	10	10	0	20
Oxford A	Sheffield C	10	0	0	10
Durham B	Southampton A	10	0	0	10
Warwick A	Oxford B	10	0	0	10
Cornell-DII	Binghamton B	10	0	0	10
Syracuse	RIT A	10	0	0	10
Binghamton A	Rochester	0	0	0	0
RIT B	ESF	10	10	0	20
Georgia Tech D	Georgia Tech A	10	10	0	20