228 CARNOT’S CYCLE IN THERMODYNAMICS.—-MACGREGOR. 
classes of substances, usually gases and substances partly in the 
liquid state and partly in the state of saturated vapour. And 
they either assume it to be true of all other classes of substances 
without any farther statement or state that it may be shewn 
to be so. These other substances, however, including simple 
substances which contract as their temperature rises and mix- 
tures of substances in the solid and liquid state, some of which 
contract while others expand on liquefaction, differ in their ther- 
mal properties in so marked a manner from both gases and satu- 
rated vapours, that it would seem to be necessary before applying 
to them the results of the study of Carnot’s Cycle, to prove that 
they too when subjected to that cycle, so as to do external 
work, absorb heat when ata high temperature and emit heat 
when at a low temperature. 
To shew how different the proofs are for substances of differ- 
ent kinds, I give them for all kinds, including those ordinarily 
given in works on Thermodynamics. In all cases I assume the 
operations of the cycle to be applied directly, 1. e., so that 
the working substance does external work. As the conditions 
of reversibility may be fulfilled equally well by all substances, 
it will follow that when so subjected to the operations of the 
cycle that work is done on the working substance by the 
external forces, heat is absorbed by the working substance when 
at a low temperature and emitted by it when at a high temperature. 
Let the variation of the 
physical state of a body when 
subjected to Carnot’s cycle be 
represented in the usual way 
on the Indicator diagram, by 
the line ABCDA, ¢ and ¢’ 
being the two adiabatics or 
isentropics, and ¢ and ¢’ the two 
isothermals, of which portions 
0 -are described by the indicating 
point during the cycle. Let 
, @, stand also for the entropy of the isentropics, and ¢ ¢ for 
the temperatures of the isothermals. 
