ENTROPY 61 



I - S{P, 0) = RInP - CT In T -\- f {C^'/T) dT + L/T (15) 



All of the terms on the right are measurable quantities, excepting that 

 Cp"' cannot be followed clear down to the absohite zero, so that the piece 

 of the integral extending from zero up to a few degrees absolute must 

 be guessed. Now at the bottom of the accessible temperature-range Cp is 

 already very small, and in most cases the curve of Cp versus T seems to be 

 heading very smoothly toward zero, so that the uncertainty is probably 

 slight. Surprises in the unreachable range are, however, not inconceivable. 



Everyone familiar with entropy will have known in advance, and on 

 reading equations (12) and (14) will have remembered, that the additive 

 constants I and S{P, 0) are beyond the reach of all experiment, be it 

 physical or be it chemical. No way can be devised of measuring them, for 

 in chemistry or in physics it is never the entropy of a system in any one 

 state which is measured, but only the difference of the entropies in two 

 different states, and the additive constant is cancelled in the subtraction. 

 So far as (12) by itself or (14) by itself is concerned, each constant is but a 

 vain appendage, and to develop a theoretical value of either would be 

 reasoning in a void. In spite of all this, the difference between / and 

 S{P, 0) is within the reach of experiment. This permits of one, or two, or 

 even of all three of the following situations: 



(a) If there is a plausible theory of entropy which leads to a value for /, 

 experiment will fix a value for S{P, 0) corresponding to that theory. 



(6) If there is a plausible theory of entropy which leads to a value for 

 S{P, 0), experiment will fix a value for / corresponding to that theory. 



(c) If there is a theory which leads to a value for S{P, 0), and there is 

 another and independent theory which leads to a value for /, then experi- 

 ment can tell whether the two are compatible. 



The actual situation is most nearly like the last of these three; and from 

 this viewpoint I will describe it. 



Before going on to the theories of / and of SiP, 0) I point out that (15) 

 is the equation of the vapor-pressure curve; for P and T occur in it as variables, 

 and it refers explicitly to such paired values of P and T as correspond to 

 points lying on the divide between solid and gas, and P for any such point 

 is called the vapor-pressure of the substance for the temperature corre- 

 sponding. Measurements of vapor-pressure are therefore the ones which 

 are called to decide on these questions — measurements of vapor-pressure 

 and of specific heat, and of the heat of vaporization. The last-named, the 

 quantity /,, need be measured at a single temperature only, for there is a 

 formula which gives its value at any temperature in terms of its value at 

 any other temperature and the specific heats over the range between. 



