Ludwig Boltzmann - Southeast

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


Brown B	Amherst B	10	0	10
BC A	Brandeis Orlando	0	0	0
BC B	Brandeis Wilson	10	10	20
BU	Brown A	10	10	20
MIT A	Brandeis Clemenceau	10	10	20
Harvard	Brown C	10	0	10
Amherst A	MIT B	10	10	20
Tufts A	Bowdoin B	10	10	20
Tufts B	Brandeis Lloyd George	10	0	10
Williams	Dartmouth	10	0	10
Yale A	Cornell-UG	10	0	10