ISOTHERMAL AND ADIABATIC CHANGES. 295 



Inasmuch as a difference of '002 in the value of y makes a difference 

 of about 1 in 0, and as the values of y obtained by different methods 

 differ by far more than this, the value of thus obtained can only be 

 regarded as an approximation justifying the use of the gas scale for the 

 absolute scale when no great exactness is required. We shall see later 

 how a much closer approximation may be found. 



The Relations between Volume, Pressure, and Temperature 

 of a Gas expanding Adiabatically. We may use the approximate 

 equation 



pv=p v (l+at) 



where R =p v a and T is the gas temperature measured from below 



a 



0. 



Now the elasticity of a substance is, by definition, 



dp 



~ V ^T 

 dv 



If T is constant 



vdp +pdv 



vdp 

 or e = -= =p 



dv 



But e+ = ye* = yp 



Hence if any small adiabatic changes of p and v occur 



vdp 



- -j = yp 



dv 



dp dv 



or = -y 



p v 



whence log p = log Cv~ 



or pv = C where is a constant. If we eliminate v by means of the 

 equation pv = HT we have 



Or if we eliminate p we have 



= R ' f 



As an illustration let us find the fall of temperature if a mass of air 

 at 15 0. expands adiabatically to double its volume, the value of y being 

 1-4. If the new temperature is T' we shall have the two equations 



-i- JL 



R ' 288 



