318 J. W. Gibhs on Graphical Methods in the 



character of which depends upon the nature of the body under con- 

 sideration. Except in the case of an ideal body, the properties of 

 which are determined by assumption, these lines are more or less 

 unknown in a part of their course, and in any case the area will gen- 

 erally extend to an infinite distance. Very much the same inconven- 

 iences attach themselves to the areas representing work in the entropy- 

 temperature diagram.* There is, however, a consideration of a gen- 

 eral cliaracter, which shows an important advantage on the side of 

 the entropy-temperature diagram. In tliermodynamic jjroblems, heat 

 received at one temperature is by no means the equivalent of the 

 same amount of h^at received at another temperature. For example, 

 a supply of a million calories at 150^' is a very different thing from a 

 supply of a million calories at 50*^. But no such distinction exists in 

 regard to work. This is a result of the general law, that lieat can 

 onljr pass from a hotter to a colder body, while work can be transferred 

 by meclianical means from one fluid to any other, whatever may be 



* In neither diagram do these circumstances create any serious difficulty in the esti- 

 mation of areas representing work or heat. It is always possible to divide these areas 

 into two parts, of which one is of finite dimensions, and tlie other can be calculated in 



tlie simplest manner. Thus, in the entropy-tem- 

 ^' ' perature diagram, the work done in a path AB 



(fig. 2) is represented by the area included by the 

 path AB, the isometric BC, the line of no pressure 

 and the isometric DA. The line of no pressure 

 and the adjacent parts of the isometrics in the 

 case of an actual gas or vapor are more or less 

 undetermined in the present state of our knowl- 

 edge, and are likely to remain so ; for an ideal gas 



"k the line of no pressure coincides with the axis of 



abscissas, and is an asymptote to the isometrics. 

 But, be this as it may, it is not necessary to examine the form of the remoter parts of 

 the diagram. If we draw an isopiestic MN, cutting AD and BC, the area MNCD, which 

 represents the work done in MN, will be equal to p{^''—v'), where p denotes the pre- 

 sure in MN, and v" and v' denote the volumes at B and A respectively (eq. 5). Hence 

 the work done in AB will be represented by KS^}A+p{v"—v'). In the volume- 

 pressure diagram, the areas representing heat may be divided by an isothermal, and 

 treated in a manner entirely analogous. 



Or, we may make use of the principle, that, for a path which begins and ends on the 

 same isodynamic, the work and heat are equal, as appears by integration of equation 

 (1). Hence, in the entropy-temperature diagram, to find the work of any path, we may 

 extend it by an isometric (which will not alter its work), so that it shall begin and end 

 on the same isodynamic, and then take the heat (instead of the work) of the path thus 

 extended. This method was suggested by that employed by Cazin (Theorie elemen- 

 taire des Machines a Air Chaud, p. 11) and Zeuner (Mechanische Warmetheorie, p. SO) 

 in the reverse case, viz: to find the heat of a patli in tlie volume-pressure diagram. 



