CHAPTER VI 



PLANE WAVES OF SOUND 



58. Elasticity of Gases. 



In any fluid there is a definite relation between the pressure 

 p, the density p, and the temperature 0, and any two of these 

 quantities accordingly serve to specify the physical state of 

 the substance. It is often convenient to use in place of p its 

 reciprocal v, the volume of unit mass. 



In thermodynamical investigations the two quantities 

 usually chosen as independent variables are p and v. In 

 Watt's " indicator diagram " these are taken as rectangular 

 coordinates, p being the ordinate and v the abscissa. Any 

 particular state is then represented by a point on the diagram, 

 and any succession of states by a continuous line. We may 

 imagine the unit mass of the fluid to be enclosed in a deform- 

 able envelope, and that an infinitesimal change of volume is 

 produced by a displacement of the boundaiy in the direction 

 of the normal, whose amount is (say) v for any given surface- 

 element 8S. The work done by the contained gas in this 

 process is 2 (p&S . v), or pSv, since 2 (v8S) = Sv. Hence the 

 work done in any succession of changes, represented by a curve 

 on the diagram, will be given by fpdv, i.e. by the area included 

 between the curve, the axis of abscissae, and the first and last 

 ordinates. This area is of course to be taken with its proper 

 sign, according as the work is positive or negative. 



There are two kinds of successions of states which are 

 specially important. In the first of these the temperature does 

 not vary, and the representative lines are therefore called 

 " isothermals." By means of a system of isothermal lines 

 drawn at sufficiently small intervals the properties of the 



