Fundamental Theorem in the Mechanical Theory of Heat, 87 

 1. The temperature t of the gas is changed to /j, which, for 



h mi jk I 



the sake of an example, may be less than t. To do this, the 

 gas may be enclosed within a surface impenetrable to heat, and 

 allowed to expand without either receiving or losing heat. The 

 diminution of pressure, consequent upon the simultaneous in- 

 crease of volume and decrease of temperature, is represented by 

 the curve ah-, so that, when the temperature of the gas has 

 reached /j, its volume and pressure have become oi and ih 

 respectively. 



2. The gas is next placed in communication with a body Kj, 

 of the temperature ^j, and allowed to expand still more, in such a 

 manner, however, that all the heat lost by expansion is again sup- 

 plied by the body. With respect to this body, we shall assume 

 that, owing to its magnitude or to some other cause, its tempe- 

 rature does not become appreciably lower by this expenditure of 

 heat, and therefore that it may be considered constant. Conse- 

 quently, during expansion the gas will also preserve a constant 

 temperature, and the diminution of the pressure will be repre- 

 sented by a portion of an equilateral hyperbola h c. The quan- 

 tity of heat furnished by Kj shall be Qj. 



3. The gas is now separated from the body K^ and allowed to 

 expand still further, but without receiving or losing heat, until 

 its temperature has diminished from t^ to t^. The consequent 

 diminution of pressure is represented by the curve c d, which is 

 of the same nature as « 6. 



4. The gas is now put in communication with a body Kg, 

 having the constant temperature tc^f and compressed; all the 

 heat thus produced in it being imparted to Kg. This com- 

 pression is continued until Kg has received the same quantity of 

 heat Qi as was before furnished by Kj. The pressure will in- 

 crease according to the equilateral hyperbola de. 



5. The gas is then separated from the body K^ and com- 

 pressed, without being permitted to receive or lose heat, until 



