POSSIBLE EFFICIENCY OF HEAT-ENGINES. 835 



Carnot's engine consists of a cylinder having no outlet nor inlet, 

 with an air-tight piston inclosing a mass of air which changes in vol- 

 ume with the movements of the piston. The piston and sides of the 

 cylinder are supposed to be perfect non-conductors, while the bottom of 

 the cylinder is a perfect conductor of heat. The engine has a source 

 of heat and a refrigerator, whose temperatures are supposed to remain 

 absolutely constant whether parting with or receiving heat. There is 

 also a non-conducting stand, on which, if the cylinder be placed, no 

 heat can enter or escape from it, however much the air within it may 

 change in temperature. In the working of the engine there are four 

 operations, as follows : 



First Operation. The air is supposed to be at the temperature of 

 the refrigerator, which may be designated by t, and to have a volume 

 represented by O a, and pressure represented by a A (Fig. 2). The 

 cylinder is supposed to stand 

 upon its non-conducting support. 

 The piston is now depressed, 

 and, since no heat can escape, 

 the air rises in temperature. 

 The compression continues till 

 the temperature of the air be- 

 comes that of the source, which 

 we designate by T. The rise in 



pressure will be represented by L J L J i X 



the adiabatic line A B. Let 



O b represent the volume and 



B b the pressure at the end of the operation. It is plain that work 



must have been done to compress the air, equal to the space swept 



through by the piston multiplied by the mean pressure ; but this is 



represented by the area of the figure A B b a. 



Second Operation. The cylinder is placed upon the source of heat 

 and the piston allowed to rise, being forced upward by the pressure of 

 the air. The bottom of the cylinder being a perfect conductor, heat 

 will enter so rapidly as to maintain the temperature of the air while it 

 expands. The pressure therefore falls, as indicated by the isothi rmal 

 line B C. Let this operation continue until an amount of heat II is 

 taken from the source, and suppose c to represent the volume and 

 c C the pressure of the air at that time. It will be seen that during 

 this operation work represented by the area B C c b will have been 

 done by the air. 



Third Operation. The cylinder is returned to its non-conducting 

 support. The upward stroke of the piston continues, and the air ex- 

 pands without receiving heat, until its temperature falls to that of the 

 refrigerator, that is, to the temperature that it had at the beginning of 

 the first operation. The fall of pressure is represented by the adia-- 

 baticC D, and work represented by the area (7 D d c is done by the air. 



Fig. 2. 



