ISOTHERMAL AND ADIABATIC CHANGES. 



287 



Equating the two areas, we get as before 



,/j avOdp 



7 



The adiabatics are steeper than the isothermals on the 



indicator diagram. If , is positive, i.e. if a body expands with rise 

 of temperature at constant pressure, then dO is positive if p is increased. 

 The adiabatic, as AB, Fig. 165, rises then from a lower to a higher 

 temperature, and must slope up more rapidly than the isothermal. 



If a is negative so is dO. In this case the isothermals for lower 

 temperatures are above those for higher temperatures, on the diagram, 

 and as the adiabatic AB rises to a lower temperature, again it must slope 

 more rapidly. 



The formula dQavOdpfK^ has been verified in various cases, first 

 by Joule for water and sperm oil (Scie?itific Papers, vol. i. p. 474), the 

 liquid being suddenly compressed in a 

 copper vessel by the addition of weights 

 on to a piston in a small connected 

 cylinder. The change of temperature was 

 determined by a thermo-electric circuit, of 

 which one junction was in the centre of 

 the copper vessel, the other in a constant 

 temperature water bath outside. To 

 justify the use of the thermoelectric 

 circuit it was necessary to prove that the 

 pressure alone did not affect the E.M.F. 

 This Joule did by having the difference of 

 temperature between the junctions in one 

 case small and in another great, and show- 

 ing that pressure produced the same effect 

 in each case. Had the E.M.F been altered 

 by the pressure the alteration would have been greater for a greater 

 temperature difference. 



We may take as a specimen an experiment on water at 30 C. 

 The pressure put on was 53,634 Ibs. per sq. ft., equivalent to 2-57 x 10 7 

 dynes per sq. cm. 



At 30 a =-00032 

 =303 

 v =1 

 Ep = 4'2 x 10 7 , the mechanical equivalent of 1 calory. 



Then by the formula we should have 



J0 -00032 x 303 x 2-57 x 10 7 



FiG. 166. Entropy-Temperature 

 diagram. 



Joule found by experiment 



4-2 x 10 7 

 = -059 



According to the formula dd should change sign with a and, other things 

 being the same, should be proportional to it. This conclusion was verified 



