ISOTHERMAL AND ADIABATIC CHANGES. 



285 



If we denote the change of pressure at constant voluma per degree rise 

 in temperature by u, then AH = (W0, and putting 



. QcW 



= <i>dd'dv 



' e 



and Q = <*>0dv. (1) 



The qtuintity u> is only observed in gases, for which it is approximately 



i- t but we can express it in all cases in terms of eg, the isothermal 

 v 



elasticity, and a, the coefficient of expansion at constant pressure. 

 Let AB be an isothermal at (Fig. 164), and let AC, CB be 

 drawn parallel to the axes, meeting at 

 C, of v. Inch the temperature is 9 dO. 

 The delinition of e<> is 



_ v x small increase of pressure 

 consequent decrease of volume 



where the changes are at constant 

 temperature 



AC 



But 



60=-. 



(2) 



FIG. 164. 



Substituting in (1) from (2) we get 

 Q = ae<,ddv. 



If we put e e dv = vdp, we get the heat in terms of the pressure 

 change, viz., 



Q = avddp. 



The heat taken in or given out by a body in passing from 

 a given condition to a neighbouring adiabatic is the same along 



all paths. Let H in Fig. 165 indicate the initial condition of the body, 

 and let BA be a neighbouring adiabatic. Let HA, HB be any two 

 different paths to the adiabatic. If the body is worked reversibly round 



HAB, then ^ = 0. Or if Qj be the heat taken in along HB, Q 2 that 



along HA, O l 2 the average temperatures at which it is taken in along 

 the two respectively, then since no heat is taken in or given out along AB 



a 



In the limit when H approaches AB, -1 = 1, and therefore Q 1 = Q 2 . 



^2 



The reader will easily see how this proposition comes out at once by 

 the use of the entropy-temperature diagram. 



The change in temperature when a body undergoes a small 

 adiabatic change of volume by a given change of pressure. Let 



