THERMODYNAMICAL SYSTEM OF GIBBS 65 



may be the nature of the working substance or of the change it 

 undergoes. The proof of these propositions given by Carnot 

 was unsatisfactory, for he adhered to the caloric theory of heat 

 and did not admit that, when work is obtained, an equivalent 

 amount of heat must disappear. Clausius, in 1850, showed 

 that their proof, in fact, involves another principle which he 

 stated as follows: "It is impossible for a self-acting machine, 

 unaided by any external agency, to convey heat from one body 

 to another at a higher temperature." Suppose that it were 

 possible to have two such reversible cyclic processes, working 

 between the same temperature limits, one of which was more 

 efficient than the other. Then in the operation of the first 

 process a quantity of heat Qi may be absorbed at the higher 

 temperature and a quantity of work W obtained. This work 

 may be used to operate the second process in the reverse 

 direction so that it absorbs heat at the lower temperature and 

 gives it out at the higher temperature. Let the amount of heat 

 given out at the higher temperature for the expenditure of 

 work W, in this cycle be Q2. Then by hypothesis, 



W/Qi > W/Q2, 



or, 



Q2 > Qi. 



Therefore the second cycle returns more heat to the heat res- 

 ervoir at the higher temperature than is absorbed in the first 

 cycle, and it would be possible by the use of the two cyclic 

 processes, without the action of any outside agency, to cause 

 heat to pass from the lower to the higher temperature, which 

 is contrary to the principle stated above. 



This principle is one of several alternative ways of stating 

 the second law of thermodynamics. We may observe that the 

 passage of heat from a hotter to a colder body is a spontaneous 

 process by which a system, which is not in a state of equilibrium, 

 proceeds towards equihbrium. Applied generally to all kinds of 

 changes, the principle may be stated in the following way: 

 Mechanical work can always be obtained when a system changes 

 from a state, which is not a state of equilibrium, into a state of 



