GIBBS' PAPERS I AND II 23 



If in place of Q', the heat given up at t', we use —Q' as the 

 heat absorbed at I', the relation becomes 



•^ + — < 



With the understanding that Qi represents the heat absorbed at 

 the temperature f » summation shows that 



2yi:S0 or j j&O 



is a statement of the second law, the equality sign holding for 

 the reversible engine. The corresponding statement of the first 

 law is 2 Qi = W or fdQ = W. 



Lecture VII (Oct. 23). The characteristic equation /(p, y, t) 

 = 0. The -pv diagram; isothermals and adiabatics. The work 

 done in a circuit is the area of the circuit. 



fdQ=fdW, f!^SO. 



Jo Jo Jo t 



If we define the energy as 



ei - €0 = / (dQ - dW), 

 Jo 



e is independent of the path since the circuit integral of dQ — dW 

 is zero. In like manner for reversible engines the quantity 



Jo 



dQ 

 ^71 — Tjo — ; — 



is independent of the path. It is called the entropy and like the 

 energy is known except for an additive constant determinable 

 when the arbitrary common origin of the paths is known. Then 



dW = pdv, de = dQ - dW, drj = dQ/t, 



dQ = tdt], dc = tdf] — pdv. 



Of the seven quantities, five, namely, t, p, v, e, r; have particular 

 values at any point of the diagram; the other two, Q, W have no 

 certain values, being dependent on the path to that point. 



