The constant pressure cycle is so called because heat is added to the working fluid at constant pressure. In this cycle adiabatic compression raises the pressure—not the temperature—from the lower to the higher limit. At the higher limit of pressure, heat is added while the working fluid expands at a constant pressure. The temperature thus increases in proportion to increase of volume. When the heat supply ceases, adiabatic expansion proceeds and reduces the pressure of the working fluid from the higher to the lower point. Again here we are dealing with pressure and not temperature. The heat in this case is discharged from the cycle at the lower pressure but at diminishing temperature. It can be shown in this case also that E = 1 − t/tc, that is, that although the maximum temperature of the working fluid is higher than the temperature of compression and the temperature at the end of adiabatic expansion is higher than the lower temperature, yet the proportion of heat convertible into work is determined here also by the ratio of the temperatures before and after compression.

The constant volume cycle is so called because the heat required is added to the working fluid at constant volume. In this cycle adiabatic compression raises the pressure and temperature of the working fluid through a certain range; the heat supply is added while the volume remains constant, that is, the volume to which the fluid is diminished by compression. Adiabatic expansion reduces the pressure and temperature of the working fluid until the volume is the same as the original volume before compression, and the necessary heat is discharged from the cycle at constant volume during falling temperature. Here also it can be shown that the thermal efficiency depends on the ratio between the temperature before compression and the temperature after compression. It is as before E = 1 − t/tc. Where t is the temperature and v the volume before compression, and tc the temperature and vc the volume after adiabatic compression, it can be shown that (vc/v)γ−1 = t/tc, so that E may be written

E = 1 − ( vc) γ−1 ,
v

and if vc/v = 1/r, the compression ratio, then

E = 1 − ( 1) γ−1 .
r

Table III.—Theoretical Thermal Efficiency for the Three Symmetrical Cycles of Constant Temperature, Pressure and Volume.

1/rE
1⁄20.0261⁄70.55
1⁄30.361⁄100.61
1⁄40.431⁄200.70
1⁄50.481⁄1000.85

Thus in all three symmetrical cycles of constant temperature, constant pressure and constant volume the thermal efficiency depends only on the ratio of the maximum volume before compression to the volume after compression; and, given this ratio, called 1/r, which does not depend in any way upon temperature determinations but only upon the construction and valve-setting of the engine, we have a means of settling the ideal efficiency proper for the particular engine. Any desired ideal efficiency may be obtained from any of the cycles by selecting a suitable compression ratio. Table III., giving the theoretical thermal efficiency for these three symmetrical cycles of constant temperature, pressure and volume, extends from a compression ratio of ½ to 1⁄100th. Such compression ratios as 100 are, of course, not used in practice. The ordinary value in constant volume engines ranges from 1⁄5th to 1⁄7th. In the Diesel engine, which is a constant pressure engine, the ratio is usually 1⁄12th. As the value of 1/r increases beyond certain limits, the effective power for given cylinder dimensions diminishes, because the temperature of compression is rapidly approaching the maximum temperature possible by explosion; thus a compression of 1⁄100th raises the temperature of air from 17° C. to about 1600° C, and as 2000º C. is the highest available explosion temperature for ordinary purposes, it follows that a very small amount of work would be possible from an engine using such compressions, apart from other mechanical considerations. It has long been recognized that constant pressure and constant volume engines have the same thermal efficiency for similar range of compression temperature, but Prof. H.L. Callendar first pointed out the interesting fact that a Carnot cycle engine is equally dependent upon the ratio of the temperature before and after compression, and that its efficiency for a given compression ratio is the same as the efficiencies proper for constant pressure and constant volume engines. Prof. Callendar demonstrated this at a meeting of the Institution of Civil Engineers Committee on thermal standards in 1904. The work of this committee, together with Clerk’s investigations, prove that in modern gas-engines up to to 50 h.p. it may be taken that the best result possible in practice is given by multiplying the air-standard value by .7. For instance, an engine with a compression ratio of one-third has an air-standard efficiency of 0.36, and the actual indicated efficiency of a well-designed engine should be .36 multiplied by .7 = 0.25. If, however, the compression ratio be raised to one-fifth, then the air-standard value .48 multiplied by .7 gives .336. The ideal efficiency of the real working fluid can be proved to be about 20% short of the air-standard values given.

(D. C.)