10 



GKAPHICAL METHODS IN THE 



general character, which shows an important advantage on the side of 

 the entropy-temperature diagram. In thermodynamic problems, heat 

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

 same amount of heat received at another temperature. For example, 

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

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

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

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

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

 the pressures. Hence, in thermodynamic problems, it is generally 

 necessary to distinguish between the quantities of heat received or 

 given out by the body at different temperatures, while as far as work 

 is concerned, it is generally sufficient to ascertain the total amount 

 performed. If, then, several heat-areas and one work-area enter into 

 the problem, it is evidently more important that the former should be 

 simple in form, than that the latter should be so. Moreover, in the 

 very common case of a circuit, the work-area is bounded entirely by 

 the path, and the form of the isometrics and the line of no pressure 

 are of no especial consequence. 



It is worthy of notice that the simplest form of a perfect thermo- 

 dynamic engine, so often described in treatises on thermodynamics, is 



represented in the entropy-temperature 

 diagram by a figure of extreme sim- 

 plicity, viz: a rectangle of which the 

 sides are parallel to the co-ordinate 

 axes. Thus in figure 3, the circuit 

 ABCD may represent the series of 

 states through which the fluid is made 



to pass in such an engine, the included 



77 area representing the work done, while 

 the area ABFE represents the heat 

 received from the heater at the highest temperature AE, and the 

 area CDEF represents the heat transmitted to the cooler at the lowest 

 temperature DE. 



There is another form of the perfect thermodynamic engine, viz : 

 one with a perfect regenerator as defined by Rankine, Phil. Trans. 

 vol. 144, p. 140, the representation of which becomes peculiarly 

 simple in the entropy-temperature diagram. The circuit consists of 

 two equal straight lines AB and CD (fig. 4) parallel to the axis of 

 abscissas, and two precisely similar curves of any form BC and AD. 



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 eUmvn,- 

 taire den machines a air chaud, p. 11, and Zeuner, Mechanische Warmetheorie, p. 80, 

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







E 

 Fig. 3. 



