52 BELL SYSTEM TECHNICAL JOURNAL 



and the best of scaling-ladders appears to be the ideal gas, as everybody 

 has used it for the purpose. 



We therefore receive the definition of the "ideal gas": a substance whereof 

 (a) the temperature remains unchanged when the gas is given and seizes the 

 chance of expanding without any hindrance into a vacuous space; and (b) 

 the pressure varies inversely as the volume, so long as the temperature 

 remains unchanged. Now rather than being an aid to enter the citadel, this 

 definition appears to presume that we are in the citadel already, since the 

 word of "temperature" is all too prominent in it. But the word comes up 

 only in the phrase "... temperature remains unchanged . . ."; so nothing 

 more is implied, than that the onlooker knows how to recognize whether 

 temperature is changing or staying the same. This ability can be his, 

 whether or not he knows about the scale called absolute; and so the defini- 

 tion implies nothing about the scale. 



The definition would be an idle collection of words, were there not actual 

 gases conforming to it so nearly, that at least for a time they may safely be 

 taken to conform to it exactly. All gases in fact approach conformity, as 

 the density lessens; and with helium and hydrogen especially, the approach 

 is already close while the density is still so high that there is no trouble at 

 all in using them as thermometers. Now, to use an ideal gas as a thermom- 

 eter means simply this: P being the pressure of the gas and V its volume and 

 n the quantity of the gas measured in moles, there is the equation, 



PV = nRT (1) 



which is a mixture of a new definition and a theorem. The part which is 

 definition is, that the temperature called absolute is taken to be proportional 

 to the product PV. The part which is theorem is, that if at the same 

 temperature we compare the product PV for equal numbers of moles of 

 various gases, its value is the same. What is denoted by R in equation (1) 

 is a universal constant. Its value is 1.985 in the customary units, which are 

 calories per degree per mole. Since now the degree of temperature has 

 appeared in this discourse, I recall that its value is fixed by the convention 

 that there are one hundred degrees from the freezing to the boiling point of 

 water; but on this I need not dwell. 



It is tacitly assumed that nothing in this definition will ever clash with 

 the threefold simultaneous definition of temperature and entropy and 

 Second Law, should we ever arrive at it. Taking this for granted, and tak- 

 ing advantage of the breach which has thus been made in the formerly 

 impenetrable surface of our definition of entropy, we now attack the con- 

 cepts of "state" and "reversible way." 



The usual way of dealing with "state" is to say that it is determined com- 

 pletely by any two of the three variables P, V, and T, which are inter- 



