290 HEAT. 



For iron at 30 we may take the quantities as approximately : 



a =-000033 



- 



6 =303 

 e. =1x10^ 

 K ;; = -l 12x4-2x10* 

 whence y = 1-009 



Experimental Determinations of y for Gases. This ratio has been the 

 subject of much research since Laplace first showed that the formula 

 for the velocity of sound, found by Newton, must be multiplied by the 

 square root of y, and it has been determined from that velocity, from 

 comparisons of the two elasticities, and from measurements of the two 

 specific heats. We shall give short accounts of some of the methods used. 



1. The velocity of sound. 



The velocity of propagation of waves of longitudinal disturbance in 

 air was shown by Newton to be U = ^elasticity / density. He supposed 

 the elasticity to be e s . 



Laplace pointed out that the elasticity used in the propagation of 

 sound waves in air is the adiabatic elasticity e t , for the alternations of 

 compression and rarefaction are so rapid and the conductivity of air is so 

 low that practically no conduction of heat takes place out of the com- 

 pressions or into the rarefactions. This supposition is confirmed by the 

 consideration (Lord Rayleigh's Sound, vol. ii. p. 26) that if heat were par- 

 tially diffused out of and into the waves by conduction, the entropy would, 

 on the whole, increase, and the operations would then not be reversible. 

 When, therefore, a rarefaction followed a compression, the work done in 

 expansion outwards would be less than that done in compression inwards, 

 and with the dissipation of energy the sound would die away. Lord 

 Rayleigh has shown that if the elasticity were only slightly below the 

 adiabatic elasticity, the rate of dying away would be very rapid. This 

 consideration only applies when there is partial conduction. With con- 

 densations and rarefactions taking place so slowly that the temperature 

 remained constant, all heat transfers would take place at the same tem- 

 perature and the entropy would remain constant. The operations would 

 therefore be reversible, and the waves would be propagated without 

 dissipation of energy. As the waves of sound are propagated with very 

 little dissipation of energy, the elasticity is either isothermal or adiabatic, 

 and not between the two. 



The former supposition, that it is isothermal, gives 



U= \/pressure density 

 = s/1013600 x 773-4 

 e 28,000 cm. per sec. 



But experiment gives between 33,100 and 33,300, say 33,200, as the 

 value at and 760 mm. Then the latter supposition, that the elasticity 

 is adiabatic, is alone admissible. 



