24 WILSON 



ART. C 



Lecture VIII. Discussion of pv diagram. To get the heat 

 Qab absorbed along a path from AtoB draw the adiabatic from 

 B and the isothermal from A intersecting in C and forming a 

 curvilinear triangle ABC. Then 



Qab = area ABC + (rjc - t?^)^^. 



The ^Tj-diagram. Isometric and isopiestic Hues. Carnot's 

 cycle a simple rectangular figure. We may draw diagrams other 

 than the py-diagram or the ^Tj-diagram for other purposes but 

 they do not have the advantage of simple areal interpretations.* 

 The energy surface e = /(rj, v) as a function of entropy and 

 volume. 



de de 



dri dv 



Lecture IX. Review of fundamental concepts. 

 Lecture X. Mathematical transformations. 



'dQ\ 



.dt/,' 



Specific heats C'p = ( — ) , C„ = ( - 



\dt/ p \ ( 



Elasticities E^ = - v(y\ Et = - v(-f) • 



Proof of Cp/Cv = Erj/Et given first by calculus as usual and 

 second geometrically by means of anharmonic ratios in the in- 

 finitesimal figure OV, OH, OT, OP formed by the intersection of 

 a fine VHTP with the isometric, adiabatic, isothermal and iso- 

 piestic issuing from a point of the py-diagram. The second 

 proof is as follows: 



f}p — Vo Vp — Vh 



PH 



* To this stage very little of the elaborate discussion of Paper I has 

 been given. And no illustrative material. The lecture jumps right to 

 Paper II. It may be particularly noted that the scale factor y was not 

 treated, nor the fij-diagram discussed at this stage in the course, though 

 they were treated in Paper I. 



