PRINCIPLES OF NAVAL ENGINEERING 



where 



Sj = total entropy of working fluid at state 



1, in Btu per° R 



Sg = total entropy of working fluid at state 



2, in Btu per°R 



Q = heat supplied, in Btu 



T = absolute temperature at which proc- 

 ess takes place, in° R 



The fact that the total entropy of an isolated 

 system must always increase does not mean that 

 the entropy of all parts of the system must al- 

 ways increase. In many real processes, we find 

 increases in entropy in some parts of a system 

 and, at the same time, decreases in entropy in 

 other parts of the system. But the important 

 thing to note is that the increases in entropy are 

 always greater than the decreases; therefore, 

 the total entropy of an isolated system must al- 

 ways increase. 



Each increase in entropy is permanent. In a 

 universal sense, entropy can be created but it 

 can never be destroyed or gotten rid of, although 

 it may be transferred from one system to an- 

 other. Every natural process that occurs in the 

 universe increases the total entropy of the uni- 

 verse, and this increase in entropy is irrever- 

 sible. The concept of the universe eventually 

 "running down" might be expressed in terms of 

 entropy by saying that the entropy of the uni- 

 verse is constantly "building up." The so-called 

 "heat death of the universe" is envisioned as 

 the ultimate result of all possible natural proc- 

 esses having taken place and the universe being 

 in total equilibrium, with entropy at the absolute 

 maximum. Such a statement need not imply a 

 total lack of energy remaining in the universe; 

 but any energy that might remain would be 

 completely unavailable and therefore completely 

 useless. 



THE CARNOT PRINCIPLE 



According to the second law of thermo- 

 dynamics, no thermodynamic cycle can have a 

 thermal efficiency of 100 percent— that is, no heat 

 engine can convert into work all of the energy 

 that is supplied as heat. The question now arises 

 as to how much heat must be rejected to a re- 

 ceiver which is at a lower temperature than the 

 source? Or, looking at it another way, what is 

 the maximum thermal efficiency that could 



theoretically be achieved by a heat engine oper- 

 ating without friction and withoutanyother of the 

 irreversible processes that must occur in all 

 real machines? 



To answer this question, Carnot, a French 

 engineer, developed an imaginary and completely 

 reversible cycle. In the Carnot cycle, all heat 

 is supplied at a single high temperature and all 

 heat that must be rejected is rejected at a single 

 low temperature. The cycle is fully reversible. 

 When proceeding in one direction, the Carnot 

 cycle takes in a certain amount of heat, rejects 

 a certain amount of heat, and puts out a certain 

 amount of work. When the cycle is reversed, the 

 quantity of work that was originally the output 

 of the cycle is now put into the cycle; the amount 

 of heat that was originally taken in is now the 

 amount rejected; and the amount of heat that was 

 originally rejected is now the amount taken in. 

 When thus reversed, the cycle is called a Carnot 

 refrigeration cycle. 



Obviously, no real machine is capable of 

 such complete reversibility, but the concept of 

 the Carnot cycle is nonetheless an extremely 

 useful one. By analysis of the Carnot cycle, it 

 can be proved that no engine, actual or ideal, 

 can be more efficient than an ideal, reversible 

 engine operating on the ideal, reversible Carnot 

 cycle. The thermal efficiency of the Carnot cycle 

 is given by the equation 



thermal efficiency: 



T — 

 work output , s 



heat input ~ T 



where Tg equals the absolute temperature at 

 which heat flows from the source to the working 

 fluid and Tj. equals the absolute temperature at 

 which heat is rejected to the receiver. 



The implications of this statement are of 

 profound importance, since it establishes the 

 fact that thermal efficiency depends only upon 

 the temperature difference between the heat 

 source and the heat receiver. Thermal efficiency 

 does not depend upon the propertiesof the work- 

 ing fluid, the type of engine used in the cycle, 

 or the nature of the process— combustion, nu- 

 clear fission, etc.— that produces the heat at the 

 heat source. The basic principle thus established 

 by analysis of the Carnot cycle is called the 

 Carnot principle, and may be stated as follows: 

 The motive power of heat is independent of the 

 agents employed to realize it, its quantity being 

 fixed solely by the temperatures of the bodies 

 between which the transfer of heat occurs. 



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