SCIENCE (and common SENSE ) 59 



Setting out from our postulates, we now arrive fairly straightfor- 

 wardly at deduced theorems we delightedly identify as precisely the 

 relations named for Boyle, Charles, etc. This is an immense correla- 

 tive achievement. Also an immense explanatory achievement: we see 

 how the behavior described by the colligative relations may be pro- 

 duced. Yet our satisfaction is not wholly unbounded. Using a model 

 of an ideal gas we arrive at Boyle's law, which applies rigorously to 

 that ideal gas but not to actual gases. Feeling we understand how the 

 law arises, we are now all the more anxious to understand why it is 

 not rigorously applicable to actual gases. 



Ordinarily quite reliable, predictions drawn from Boyle's law are 

 apt to be wide of the mark with gases at high pressures and/or low 

 temperatures. For such failures the relation itself offers no rationale: 

 Boyle's law simply fails, by a larger or smaller margin, under con- 

 ditions we must then memorize. But with the kinetic theory in hand 

 we can understand these failures: we have only to grasp how actual 

 gases may differ from our hypothetical ideal gas. Our gas model 

 involved two assumptions that cannot be perfectly sound. Boyle's 

 law fails under precisely those conditions in which the assumptions 

 would he least satisfactory. There is failure ( 1 ) when the gas pres- 

 sure is high and the gas volume small, so that the fraction of the total 

 volume "filled" by the corpuscles becomes significant; and (2) when 

 the gas temperature is low, so that the kinetic energy of the cor- 

 puscles no longer wholly overrides inter corpuscular attractions. In 

 the shortcomings of the assumptions used in its theoretical deriva- 

 tion, we see the origin of the shortcomings of the empirical law. No 

 longer need we simply memorize the conditions in which Boyle's law 

 fails badly; we now understand in advance that under such condi- 

 tions it must fail. 



A more sophisticated theoretical construction does without the two 

 simplffying assumptions, and yields a new (van der Waals) relation: 



(P + V2) (^ — ^) ^^ constant. From measurable characteristics of 



any gas at its critical point, we calculate a correction term ( h ) rep- 

 resenting the volume "filled" by the corpuscles themselves, and an- 

 other term {a) representing the inter corpuscular attractions. When 

 the volume of the gas (V) is large— i.e., at low pressure {p) and/or 

 high temperature— the correction terms involving a and h are negli- 

 gible, and the van der Waals relation then simply reduces to Boyle's 



