CARNOT’S CYCLE IN THERMODYNAMICS.—MACGREGOR. 229 
In the case of an ordinary substance which expands with rise 
of temperature at constant pressure, ¢ is obviously a higher 
isothermal than ¢, and ¢’ a higher isentropic than >. Hence, 
during the operation A B heat is absorbed, the substance being 
at a high temperature, and during the operation C D heat is 
emitted, the substance being at a low temperature. 
In the case of a substance which contracts with rise of temper- 
ature at constant pressure, ft is a higher temperature than ¢. For 
as a greater volume corresponds to a lower temperature, a straight 
line drawn in the direction of Ov (the axis of volumes) must 
meet successively isothermals of lower and lower temperature. 
Also in this case, ¢ is a higher isentropic than ¢. For, in order 
that such a substance may be made to expand at constant pres- 
sure, heat must be taken from it; and therefore a straight line 
drawn in the direction O v must meet successively adiabatics of 
lower and fower entropy. It follows that in the case of sub- 
stances which contract with rise of temperature, heat is emitted 
during the operation AB, and absorbed during the operation CD ; 
but in this case the temperature during the operation AB is 
low, and that during CD is high. 
In the case of a substance consisting of a mixture of a liquid 
and its vapour, AB and DC are straight lines, parallel to the axis 
of volumes. Since the saturation pressures of all vapours in- 
crease with the temperature, ¢’ is a higher temperature than t. 
And since evaporation at constant pressure invariably increases 
the volume of a substance and involves absorption of heat, ¢’ is 
a higher isentropic than ¢. Hence, in this case, heat is absorbed 
during AB when the working substance is at a high temperature, 
and emitted during CD when it is at a low temperature. 
In the case of a working substance which is partly in the 
solid and partly in the liquid state, and which contracts on lique- 
faction, AB and DC are straight lines, parallel to the line of 
volumes. For the absorption of heat at constant pressure 
diminishes the volume. It follows from this consideration also 
that ¢ is a higher isentropic than ¢’, for it cuts a line parallel 
to Ov at a point nearer Op than ¢’ dees. As the working sub- 
stance in this case is always at the melting point, ¢’ and ¢ are 
