Page:Popular Science Monthly Volume 17.djvu/855

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835
POSSIBLE EFFICIENCY OF HEAT-ENGINES.

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 volume 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 PSM V17 D855 Temperature and pressure graph.pngFig. 2. 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 becomes that of the source, which we designate by T. The rise in pressure will be represented by 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 isothermal line B C. Let this operation continue until an amount of heat H is taken from the source, and suppose O 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 expands 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 adiabatic C D, and work represented by the area C D d c is done by the air.