446 RICE 



ART. K 



Here we make a natural generalization and assume that for any 

 change of state of a homogeneous solid 



de = td-n + Xirf/i . . . + Xed/e. (40) 



Fully interpreted this means that we consider e and 17 to be 

 functions of t, /i, ... /e. Strictly we should write them 

 i{t, fi, ... /e) and r){t, fi, ... /e). If the state of the solid alters 

 to another state of equilibrium in which the variables change 

 to t + dt, /i + dfi, . . . /e + dfi, then equation (40) connects 

 the various differentials. 



It will help us if we briefly recall how from equation (39) we 

 derive the equations which connect those thermal and mechani- 

 cal properties of fluids which can be observed and measured by 

 experimental methods. Thus 



c,{t, v) lit, v) 



dr] = — - — di + — - — dv, (41) 



L If 



where c„ is the specific heat at constant volume, and U the so- 

 called latent heat of change of volume at constant temperature. 

 We are, at the moment, taking t and v as the variables and 

 indicating this precisely by writing the symbols in brackets 

 after each quantity to show that in each case we are considering 

 the appropriate functional form which expresses that quantity 

 in terms of these variables. This device will also indicate 

 without any ambiguity what quantities are being regarded as 

 constant when we write down any partial differential coefficient. 

 From the equation 



deit, v) = tdr](t, v) — p{t, v)dVf 



we derive the differential equation of the Gibbs yf function (free 

 energy at constant volume), viz., 



d^{t, v) = -7](t, v) dt - pit, v)dv, (42) 



where 



ip = € — trj. 



