ENTROPY CALCULATIONS AT LOW TEMPERATURE GEORGE CALINGAERT Hobart and William Smith Colleges, Geneva, New York
THEcalculation of the absolute entropy of solids is based on a knowledge of specific heats from absolute zero up to the desired temperature. Actual measurements go down t o only 50°K. or a t best 10°K., and the student is advised in the textbook problems to make use of the Debye formula: TS C = 465 0'
t o calculate the specific heat C between absolute zero and the lowest tem~eraturea t which C has been determined. Since this evaluation of Cis only incidental to the calculation of the desired entropy S, it may be by-passed altogether, using the following considerations:
0 is a constant characteristic of the substance; hence for any particular substance the Dehye formula is:
Expressing the entropy S and integrating, we obtain:
Stated in words: The entropy at any temperature up t o which the Debye formula applies is equal to one-third of the specific heat a t that temperature. The relationship must no doubt have been made use of in calculations, but no reference t o it has been found in the physical chemistry textbooks.
