ENTROPY 



59 



zontal axes, but no coordinate-scales are shown, and no attempt has been 

 made to shape the curves in exactly the manner correct for any particular 

 substance, since all that matters here is the general idea. Envisage any 

 point (P, T) in the area "gas," lying just off the curve which separates that 

 area and the other one marked "solid." This is the point — I will call it 

 the "point of interest" — for which we are to obtain two expressions for 

 entropy S arising from different sources, and find an important result by 

 comparing the two so obtained. 



One of the two is of course the right-hand member of (12). It may 

 create surprise that one should be treating the gas as ideal, under condi- 

 tions where the slightest fall in temperature or rise in pressure would con 



Fig. 1 



dense it. The approximation, however, may still be a good one, and if it is 

 not close, the equation of state of the actual gas may be used in place of (1). 

 To form the other expression, we commence at the point (P, 0) where 

 the isobar P which traverses the point of interest reaches the vertical axis, 

 and call the entropy there by the symbol S{P, 0). We proceed along the 

 isobar toward the point of interest, building up the integral f (Cp/T)dT; 

 since we remain in the area called "solid," it is C,, of the solid which con- 

 cerns us, and we may mark it so. Just before the isobar passes over the 

 curve dividing solid from gas, the entropy arrives at the value 



s{p, 0) + r {c;'/r) dT 



Jo 



but this is not yet the value at the point of interest, for the "divide" is yet 

 to be crossed. At the crossing of the divide a certain amount of heat is 



