Fourth Operation—. The cylinder is placed upon the refrigerator, the piston caused to descend, and the air compressed until its initial volume is reached. Since the bottom of the cylinder and the refrigerator are supposed to be perfect conductors, the heat generated by the compression will escape to the refrigerator, and the temperature of the air will remain constant. The air is now in the same condition as regards temperature, volume, and pressure, as at the beginning of the first operation. The isothermal line, which represents the rise of pressure during the last operation, must, therefore, pass through the starting-point A. During this operation work represented by the area A D d a must be done upon the air, and a certain amount of heat—all that generated by compressing the air—must be given up to the refrigerator.
It will be noticed that, during the second and third operations, work represented by the area B C D d b is done by the air, and during the first and fourth operations work represented by B A D d b is done upon the air. During the complete cycle of operations, therefore, mechanical effect is developed equivalent to the difference between these areas, or to the area B C D A. This figure is, in fact, the indicator diagram of the engine. During the second operation, heat represented by H was taken from the source, and during the fourth operation heat represented by h was given to the refrigerator. During the cycle of operations, heat equal to H—h has disappeared, and, since the working substance is at the end of the cycle in precisely the same condition as at the beginning, this heat must be the equivalent of the mechanical effect developed, and the efficiency of the engine is H
But it is easily shown that this cycle of operations is a completely reversible cycle. For suppose the substance at its initial volume O a, pressure A a, and temperature t. Place the cylinder on the refrigerator, and allow the air to expand to the volume A d. The same isotherm A D that represented the rise in pressure in the reverse operation will now represent the fall, and the same heat h that was before given to the refrigerator will now be taken from it. Now let the cylinder be placed upon its non-conducting support and the piston descend till the volume becomes O c. Since no heat escapes, the rise of pressure will be represented by the adiabatic D C, and the temperature will rise by the same amount as it fell during the expansion from c to d, that is, from t, the temperature of the refrigerator, to T, that of the source. Now, let the cylinder be placed upon the source, and the descent of the piston continue till the volume of the air becomes O b, the temperature remains that of the source, the isotherm C B represents the rise in pressure, and heat is given to the source precisely equal to the amount taken from it during the expansion from b to c in the direct working of the engine. Now let the cylinder be placed upon its non-conducting support, and the piston rise till the volume becomes O a.