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Challenge: Problem 4

Consider the situation in the physics of the specific heat of solids around the time of Planck's discoveries. Dulong and Petit had made empirical studies, around 1820, which had led to the generalization that the specific heat per gram molecule of solid is 6 cal deg.. This result was easily intelligible in terms of the Array item ( = T ). A gram atom of any solid contains the . If each of these always has an average energy of T, then the specific heat per gram atom of any substance should always be the same.

By 1900, the extension of the experimental work had produced data on the specific heats of solids such as that shown in the graph here. It is obvious that the specific heat decreases rapidly with decrease of temperature at low temperatures, and that this variation differs from substance to substance. At low temperatures ("low" relative to the particular solid) it seemed that only a fraction of the matter was involved in the plane of thermal phenomena. Again, Einstein made the first step towards a resolution of these theoretical difficulties.

Can you work out a possible way in which these "anomalies" in the specific heats of solids could have been explained? Concentrate on the essential points, and select those items on the RESPONSE ARRAY which you think are relevant.

1
the number of antinodes in the range v to v + dv is ( ( 8 v2 ) / c3 ) dv 		2
radiation pressure p = 1/3 u where u is the energy density		 3
E = T 4 (a form of the Stefan-Boltzmann law)		 4
max T = constant (Wien's displacement law)		 5
fluctuations of energy
6
the energy distribution of radiation is not a function of temperature alone		 7
characteristic vibrational frequency of a material particle's energy state		 8
exchanges of energy in discrete amounts		 9
spectrum of ionized gas		 10
continuum of energy changes
11
one-way emission of radiation		 12
av < 1 (absorbtivity less than one)		 13
a coloured surface often emits its complementary colour when heated		 14
characteristic radiation pattern of a surface for a given temperature		 15
as T decreases below a certain value for a solid, so does its specific heat
16
monochromatic radiation, as obtained by using a filter		 17
= ( hv / ( e ( h v / k T ) - 1 ) )		 18
= n 0		 19
= hv		 20
= kT