128 INTRODUCTION TO IMMUNOCHEMICAL SPECIFICITY 



functions of P and /', such that when both sides of equation ( 10 ) are 

 multipHed by one of them, the product B dQ becomes an exact 

 differential. In the present case such a function is easily found. The 

 simplest one is \/T. Multiplying by \/T, we obtain 



dQ/T = [{dE/dV + P)/T]dV + [{dE/dP)/T]dP (11) 



That dQ/T is an exact differential is proved in thermodynamics 

 (Klotz, 1950) by showing that dQ/T is an exact differential (a) 

 for an ideal gas carried through a certain sequence of reversible 

 changes called a Carnot cycle, (b) for any substance carried through 

 a Carnot cycle, and (c) for any substance carried through any re- 

 versible cycle. 



The sequence of changes which constitute a Carnot cycle is so 

 simple and symmetrical that it is easy to show that, for such a cycle 

 and by virtue of part (c) of the above-mentioned proof for any 

 reversible cycle, 



W/Q2 = {T, - T,)/To (12) 



where W is the work done by the system during the cycle, Qo is 

 the heat taken in at the higher temperature To, and Ti is the lower 

 temperature. The fraction W/Qo is called the efficiency of the cycle. 

 In thermodynamics it is further proved that (a) the efficiency of 

 a real substance carried through a Carnot c}-cle cannot be greater 

 than that of an ideal gas and cannot be less, and (b) the efficiency 

 of any substance carried through any reversible cycle is the same as 

 that of an ideal gas carried through a Carnot cycle. The fraction 

 IV/Q2 is therefore the maximum theoretical efficiency of any heat 

 engine which takes in heat Qo at temperature To and returns part 

 of the heat to the surroundings at temperature T]. The efficiency of 

 an actual engine will be less than this : it is impossible for the 

 efficiency of any engine, actual or theoretical, to be more. 



Since dQ/T is an exact differential, it can be integrated. As a 

 result of this integration we shall obtain a function of the independent 

 variables P and V. This is a new thermodvnamic function, and we 

 can give it a name. The name of the new function is entropy. It is 

 represented by the symbol S. and we write 



dS = dQ/T (13) 



