specific heat - 2025 ACF Fall

Question

Einstein’s model of this quantity was derived by treating each atom in a solid as three quantum harmonic oscillators. For 10 points each:

[10e] What quantity, denoted c, equals the amount of energy required to raise the temperature of one gram of a material by one degree Celsius?

ANSWER: specific heat [or specific heat capacity; reject “heat”]

[10h] Einstein’s model first calculates the multiplicity of a solid using binomial coefficients, then uses this ubiquitous approximation in statistical mechanics to simplify the logarithm of a factorial.

ANSWER: Stirling’s approximation

[10m] Debye’s (“duh-BYE’s”) model of heat capacity, which is more accurate at low temperatures, assumes energy is carried by these quasiparticles. These quasiparticles represent vibrations in a solid and can be “acoustic” or “optical.”

ANSWER: phonons [accept acoustic or optical phonons]

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Summary


Southern California	Main	Y	3	30.00	100%	100%	100%
Eastern Canada (1)	Main	Y	3	13.33	67%	67%	0%
Great Lakes	Main	Y	6	16.67	67%	67%	33%
Lower Mid-Atlantic	Main	Y	5	14.00	100%	40%	0%
Upper Mid-Atlantic	Main	Y	6	15.00	67%	67%	17%
Midwest	Main	Y	7	14.29	71%	57%	14%
North	Main	Y	4	17.50	100%	50%	25%
Northeast	Main	Y	1	0.00	0%	0%	0%
Pacific	Main	Y	4	10.00	75%	25%	0%
South Central	Main	Y	4	10.00	75%	25%	0%
Southeast	Main	Y	6	13.33	67%	50%	17%
UK (North)	UK	Y	2	10.00	100%	0%	0%
UK (South)	UK	Y	1	10.00	100%	0%	0%
Upstate NY	Main	Y	1	0.00	0%	0%	0%

Data


UCLA A	UCLA B	10	10	10	30
Claremont A	UC Irvine	10	10	10	30
UCLA C	UCLA E	10	10	10	30
Ottawa A	McGill E	0	0	0	0
Carleton A	Ottawa C	10	0	10	20
CWRU D	Ohio State D	10	0	0	10
CWRU B	Louisville C	10	10	10	30
Pittsburgh	Michigan A	10	0	0	10
Michigan B	Kentucky	0	0	10	10
Louisville A	Michigan State B	10	0	10	20
Ohio State A	CWRU A	0	10	10	20
McGill A	Ottawa D	10	0	10	20
William & Mary B	Liberty B	10	0	0	10
UNC D	Liberty C	10	0	0	10
UNC C	NCSU B	10	0	0	10
Virginia Tech C	Virginia A	10	0	10	20
William & Mary A	William & Mary C	10	0	10	20
George Mason B	George Mason C	0	0	0	0
Penn	Maryland B	10	0	10	20
Rutgers C	NYU A	0	0	0	0
NYU B	Maryland A	10	0	10	20
George Mason A	Rowan	10	0	10	20
Princeton	Stony Brook	10	10	10	30
Purdue A	Chicago A	10	0	10	20
William Woods University A	Illinois Canada	0	0	10	10
Illinois Orange	WashU Grizzlers	10	10	10	30
Iowa A	Indiana B	10	0	0	10
Illinois Blue	Purdue B	10	0	10	20
Indiana A	Purdue D	0	0	0	0
WashU Grolars	Illinois Champaign	10	0	0	10
Iowa State	Wisconsin B	10	0	10	20
Macalester	Minnesota	10	0	0	10
Wisconsin A	St. Thomas	10	10	10	30
Michigan Tech	Wisconsin C	10	0	0	10
Southern Connecticut State University A	Boston University B	0	0	0	0
Alberta A	Texas	10	0	10	20
Arizona State A	Washington Masu	10	0	0	10
Washington Chinook	Arizona State B	10	0	0	10
Washington Atlantic	Washington Steelhead	0	0	0	0
Central Oklahoma A	Kansas State A	10	0	0	10
Harding	Murray State College B	0	0	0	0
Nebraska B	Tulsa A	10	0	0	10
Murray State College A	Tulsa B	10	0	10	20
Vanderbilt A	Auburn B	10	0	10	20
Georgia Tech B	Alabama A	10	0	0	10
Georgia Tech C	Georgia Tech F	10	10	10	30
Tennessee Tech	Sewanne	0	0	0	0
Tennessee A	Emory A	0	0	10	10
Georgia Tech E	Vanderbilt C	10	0	0	10
Durham D	Durham B	10	0	0	10
York	Edinburgh A	10	0	0	10
Imperial A	Cardiff	10	0	0	10
RIT B	RIT A	0	0	0	0