40 IDEAL AND ACTUAL GASES 93 



exactly as represented in 39. Joule and Lord Kelvin 

 have measured with great care the alterations of tem- 

 perature that occur in the vessels from and to which the 

 flow takes place, and by these observations have proved that 

 the whole amount of work done by the gas in the receiver, 

 when it flows out, is not to be found in the increased energy 

 of the gas in the outer vessel which has been warmed by 

 compression, and in the heat that has been produced by the 

 overcoming of frictional resistances. This phenomenon has 

 no explanation on our theory so far as it has been developed 

 in the preceding chapters ; it proves, therefore, that a 

 secondary circumstance has not been sufficiently taken into 

 account, and scarcely leaves room for doubt that the cause 

 which has been neglected is the cohesion of the gases, to 

 overcome which during their expansion into vacuum a part 

 of the heat energy must be taken up. 



If we take in hand a thorough comparison of the two 

 laws which bear Gay-Lussac's name with the results of 

 experiment, we see no less clearly that our theory has not 

 so far led us to absolutely strict laws of nature, but only to 

 rules that hold good approximately, though the approxima- 

 tion is certainly excellent. 



According to the first of these, all gases are to expand 

 equally under the action of heat ; they ought, therefore, all 

 to have the same coefficient of expansion as air, viz. 

 0-00367. But the value of this coefficient is, for instance, 

 0-00366 for hydrogen and 0-00370 for carbonic acid. Similar 

 deviations, which in some cases are even larger, are exhibited 

 by other gases too. 



Indeed it cannot be said of any one and the same gas 

 that under all circumstances it has the same coefficient of 

 expansion. Magnus 1 has pointed out that the coefficient 

 of expansion must vary if Boyle's law is not exactly 

 obeyed. For if the pressure and volume of a gas are not 

 strictly inversely proportional to each other, there is no 

 reason to expect that both magnitudes will be increased in 

 exactly the same ratio by a rise of temperature. We have 

 therefore, strictly speaking, two different thermal coefficients 



1 Pogg. Ann. Iv. 1842, p. 5. 



