GENERAL PRINCIPLES 49 



A quantity of steam having a quantity of heat Q is taken from 

 a boiler and supplied to an engine at an absolute temperature 

 T. It produces work, and the remainder having heat Q' goes to 



the condenser at a temperature T'. But it is known that }j( or ~ 



heat energy 



expresses the entropy = - Consequently 



temperature difference . 



the engine receives a quantity of entropy ^ and gives up another 

 M-/ The quantity of heat transformed into work Q Q' is a 



fraction ** Q^ of the total quantity furnished by the source of 



heat. 



In order that the above fraction may be a maximum, it is neces- 

 sary that during the transformation no loss of heat (by radiation 

 or conduction) should take place, and also that the fall of tem- 

 perature should take place gradually from T to T', and that 

 the water should be brought gradually from T' to T. In other 

 words, the water must accomplish a complete cycle which will 

 bring it back to its initial state. The change of temperature is, 

 necessarily, very slow, so that the machine may be at any moment 

 nearly in equilibrium and be able to function in either direction, 

 thus being reversible. 



To effect the maximum work, a heat engine must perform 

 a complete and reversible cycle, this being known as the 

 Carnot Cycle. Throughout the cycle Q and T vary in such 



a way that the entropy does not change in becoming as it is 



conserved. The principle of Carnot is also called the principle 

 of the conservation of Entropy : 



2=^: therefore Q' = Q X ~ 



And the fraction transformed into work - =-^ will have as its 

 expression 



Q 



But if, somewhere, there is loss of heat, the entropy is not 

 conserved, it tends to diminish. 



36. Thermodynamics : Energetics. The two principles which 

 register the relations of heat and of work constitute thermo- 



