836 THE POPULAR SCIENCE MONTHLY. 



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 refrigera- 

 tor 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 pres- 

 sure during the last operation, must, therefore, pass through the start- 

 ing-point A. During this operation work represented by the area A 

 I) 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 re- 

 frigerator. 



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 hjBADdb is done 

 upon the air. During the complete cycle of operations, therefore, me- 

 chanical 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 represent- 

 ed by iJwas 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 II h has disappeared, and, since the work- 

 ing substance is at the end of the cycle in precisely the same condi- 

 tion as at the beginning, this heat must be the equivalent of the me- 

 chanical effect developed, and the efficiency of the engine is Hh 



H 



But it is easily shown that this cycle of operations is a completely 



reversible cycle. For suppose the substance at its initial volume a, 

 pressure A a, and temperature t. Place the cylinder on the refrigera- 

 tor, and allow the air to expand to the volume A d. The same iso- 

 therm A D that represented the rise in pressure in the reverse opera- 

 tion 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 cyl- 

 inder be placed upon its non-conducting support and the piston descend 

 till the volume becomes c. Since no heat escapes, the rise of pressure 

 will be represented by the adiabatic I) 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 de- 

 scent of the piston continue till the volume of the air becomes b, the 

 temperature remains that of the source, the isotherm C B represents 

 the rise in pressure, and heat is given to the source j)recisely 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 a. 



