THERMODYNAMIC AL SYSTEM OF GIBBS 87 



well be expressed by taking sulphuric acid and water, or sulphur 

 trioxide and water, as components, but sulphur, oxygen and 

 hydrogen are not admissible as components as their amounts 

 cannot be independently varied . The change in the value of f 

 of this mass when the amounts of Si, S2,. . .Sn are increased 

 by dmi, drui, . . . drrin, the temperature and pressure remaining 

 constant, is given by 



dr = ( -, — 1 • dmi + I - — ) • dvii 



\(l17li/ 1, p, mj, etc. \CtWl2/ «. p, mi, m,, etc. 



■ ■-+(r~) -^^"^ (^0) 



\(tmn/t, p, m„ . . . m„_i 



and we may write 



(^) 



\dmijt. 

 \dmi/t. 



= Ml, 



p, ntj, etc. 



= jU2, etc., 



p, nil, wij, etc. 



(41) 



so that 



{d^)t,p =nidmi + M2^m2 . . . + findvin. (42) 



When the temperature and pressure also vary, by combining 

 with (38), we have 



d^ = —r]dt-\- vdp + iJ.idmi + ju2C?W2 . . . + tindnin, (43) [92] 

 whence, by (38), 



de = idt] — pdv + mdmi + Hidrrh . . . + UndrUn, (44) [86] 

 and by (35) 



d}p = —rjdt — pdv + fjiidmi + HidTm . . . + Undrrin. (45) [88] 



The definition of mi, etc., given above, corresponds to the most 

 familiar condition, viz., that of constant temperature and pres- 

 sure. Since f is the free energy of the homogeneous mass, the 

 quantity 



(—) 



\dnhjl, p, m.,, . . . m,. ^ 



