LAWS OF THERMODYNAMICS 165 



One could generalize to complex, nonmolar quantities of varied composi- 

 tion; the law would still be conceptually the same: 



AU = q - w 



More will be said about this generalization later. 



The first law can be extended into a more useful form for processes taking 

 place at constant pressure. Since any substance, this book, for example, has 

 an individual and independent existence in space, and since it occupies a 

 certain volume and has an area upon which the air pressure (i.e., weight of 

 the column of air above it) is 15 lb/sq in., the book does not have as much 

 internal energy as it would have if it were in a vacuum, because it already 

 has done a considerable amount of work against atmospheric pressure. That 

 is, it has already expended enough energy (or "work of expansion"), W, to 

 roll back the atmosphere and create a hole or vacuum in which it can exist. 

 Hence the internal energy 



U = KE + PE - W 



The work of expansion, W, can be easily evaluated. Consider the cylinder 

 with frictionless piston of area, A, enclosing a volume of gas, V. From the 

 definition of work: 



Work = force x distance 



= PA x AV/A 



= PA V = P( V 2 - V, ) 



Since we are considering an initial state, V v of zero volume, in general 

 W = PV. Substituting, 



U = KE + PE - PV 



= H - PV 



where H is the internal energy contained per mole in a vacuum (when 

 P = 0). The quantity, H, is called heat content, or preferably enthalpy because 

 really potential energy as well as heat kinetic energy is included. 



A little thought about the definition will lead one to the conclusion that H 

 should be a very useful quantity for comparison purposes because its value 

 is independent of any volume change which may accompany a transforma- 

 tion or process. Further, for the case of chemical reactions, AH = H 2 - //, 

 (note the parallel with A U) must be identical with q, the heat taken in dur- 

 ing the process for the case in which the only work done is that of expansion; 

 i.e., q = AH. Many biological processes occur in solution, with no appreci- 

 able change in volume, and in these cases AU = AH. 



