of " 7 " /or a Perfect Gas. 167 



Let the work done in compressing the gas be dW; and W, 

 the kinetic energy after compression. Then, since the gas is 

 a perfect one, 



W 1 = W + dW 



= W +p dv in the limit. 

 Now, by a well-known relation, we have 



pv =§W, 



' Pl v x 



_pv + %pdv 

 v — dv 



,} 



/- 2 dv\/. dv\ 

 / 5 <fo\ 



, 5 dv 



Therefore the isentropic elasticity 





|e, 



5 



So that 7= q f° r a ^ Perfect gases. 

 o 



