PROCEEDINGS 
OF THE 
NATIONAL ACADEMY OF SCIENCES 
Volume 4 FEBRUARY 15, 1918 Number 2 
THE HEAT CAPACITY OF ELECTRO-POSITIVE METALS AND 
THE THERMAL ENERGY OF FREE ELECTRONS 
By Gilbert N. Lewis, E. D. Eastman and W. H. Rodebush 
Chemical Laboratory, University of California 
Communicated December 26, 1917 
According to the classical principle known as the equipartition of energy 
the kinetic energy of every kind of atom which is capable of motion in any 
direction is the same, and the change in this kinetic energy for a change in 
temperature of one degree is 3R/2 calories per gram atom. If in a solid sub- 
stance each atom instead of moving freely vibrates about a more or less fixed 
position according to the laws of a simple oscillator, it will possess on the aver- 
age a potential energy equal to its kinetic energy, and, if we consider the simple 
case in which the volume is kept constant the heat capacity per gram atom 
should be equal to 3R, or 5.97 calories per degree. 
According to the empirical law of Dulong and Petit, the atomic heat capacity 
at constant pressure is the same for most solid elements and equal to a little 
over 6 calories per degree. Lewis 1 calculated by means of a thermodynamic 
equation the difference between C P and C v and found for a considerable num- 
ber of elements that C v is more nearly constant and that its average value at 
20°C, when a few elements of low atomic weight are omitted, is 5.9, which is 
almost identical with the theoretical value. 
Much recent work, both experimental and theoretical, has shown that 
the earlier formulation of the equipartition law can no longer be considered 
as universally valid but rather as the expression of a limiting law which ap- 
proaches complete validity the higher the temperature, the heavier the atom 
and the weaker the constraints operating upon the atom. 2 Every factor 
which causes a deviation from the equipartition law leads to a smaller specific 
heat than the one calculated by that principle. If therefore we find for any 
substance a value of C v greater than 3R per gram atom we are led immedi- 
ately to consider the possibility that in addition to the atoms other particles, 
either inside or outside of the atoms, are acquiring thermal energy. 3 
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