88 M. R. Clausius on a modified Form of the second 



its temperature rises from t^ to its original value t, the pressure 

 increasing according to the curve ef. The volume o w to which 

 the gas is thus reduced is smaller than its original volume o h, 

 for the pressure which had to be overcome in the compression d e, 

 and therefore the work to be spent, were less than the corre- 

 sponding magnitudes during the expansion be; so that, in order 

 to restore the same quantity of heat Qj, the compression must 

 be continued further than would have been necessary merely to 

 annul the expansions. 



6. The gas is at length placed in communication with a body 

 K, of the constant temperature t, and allowed to expand to its 

 original volume o h, the body K replacing the heat thus lost, the 

 amount of which may be Q. When the gas reaches the volume 

 h with the temperature ty it must exert its original pressure, 

 and the equilateral hyperbola, which represents the last diminu- 

 tion of pressure, will precisely meet the point a. 



These six changes together constitute a circular process, the 

 gas ultimately returning to its original condition. Of the three 

 bodies K, K^ and Kg, which throughout the whole process are 

 considered merely as sources or reservoirs of heat, the two first 

 have lost the quantities of heat Q and Qj, and the third has 

 received the quantity Qj, or, as we may express it, Q| has been 

 transferred from Kj to K^, and Q has disappeared. The last 

 quantity of heat must, according to the first theorem, have been 

 converted into external work. The pressure of the gas during 

 expansion being greater than during compression, and therefore 

 the positive amount of work greater than the negative, there has 

 been a gain of external work, which is evidently represented by 

 the area of the closed figure abcdef. If we call this amount 

 of work W, then, according to equation (I), 



Q=A.W. 



The whole of the above-described circular process may be re- 

 versed or executed in an opposite manner by connecting the gas 

 with the same bodies and under the same circumstances as be- 

 fore, executing the reverse operations, i. e. commencing with the 

 compression af, after which would follow the expansions fe and 

 e d, and lastly the compressions dc,cb and b a. The bodies K and 

 Kj will now evidently receive the quantities of heat Q and Q,, 

 and Kg will lose the quantity Q, . At the same time the nega- 

 tive work is now greater than the positive, so that the area of 

 the closed figure now represents a loss of work. The result of 

 the reverse process, therefore, is that the quantity of heat Qi has 

 been transferred from Kg to K,, and the quantity of heat Q, 

 generated from work, given to the body K. 



In order to learn the mutual dependence of the two simulta- 



