THERMODYNAMICS OF FLUIDS. 9 



the condition that y = 1 throughout the whole diagram, may be seen 

 by reference to page 5. 



The Entropy-temperature Diagram compared with that in 



ordinary use. 



Considerations independent of the nature of the body in question. 



As the general equations (1), (2), (3) are not altered by interchang- 

 ing v, p and W with q, t and H respectively, it is evident that, 

 so far as these equations are concerned, there is nothing to choose 

 between a volume-pressure and an entropy-temperature diagram. In 

 the former, the work is represented by an area bounded by the path 

 which represents the change of state of the body, two ordinates and 

 the axis of abscissas. The same is true of the heat received in the 

 latter diagram. Again, in the former diagram, the heat received is 

 represented by an area bounded by the path and certain lines, the 

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

 eration. 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 generally 

 extend to an infinite distance. Very much the same inconveniences 

 attach themselves to the areas representing work in the entropy- 

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



*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 the other can be calculated in 

 the simplest manner. Thus in the entropy-tempera- 

 ture 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 knowledge, and are likely to remain so ; for 

 an ideal gas 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 Fig. 2. 



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(tf - 1/), where p denotes the pressure 

 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 ABNM+p(t/'- 1/). 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 



