Page:Elementary Text-book of Physics (Anthony, 1897).djvu/260

346 $$R.$$ The operation is continued until the volume and pressure of the body are again denoted by the point $$A.$$ During this operation the quantity of heat h is transferred from the body to the refrigerator. These operations constitute a cycle, for the body at the end of the operation is in the same condition as regards pressure, volume, and temperature as it was at the beginning. The work done by it is therefore equal to the heat transformed into work, or to $$H - h.$$

Such a cycle is reversible, for if the body be constrained to go through the operations just described, in the reverse order, the same quantities of heat will be transferred in opposite senses and the same quantity of work done upon the body that, in the direct operation, was done by the body. That is, the refrigerator will give up the quantity of heat h, the source will receive the quantity of heat $$h,$$ and the amount of work $$H - h$$ will be done upon the body. The only difference between the two operations will be that, whereas in the direct operation the temperature of the body was infinitesimally lower than that of the source while it was receiving heat, and infinitesimally higher than that of the refrigerator while it was emitting heat, in the reversed operation the temperature of the body is infinitesimally lower than that of the refrigerator while it is receiving heat, and infinitesimally higher than that of the source while it is emitting heat. These infinitesimal differences may be neglected, and one of these operations may be considered in every respect the reverse of the other.

229. Second Law of Thermodynamics.—We will now prove a most important proposition, due to Carnot, the founder of the theory of thermodynamics. To do this we make use of a principle first laid down by Clausius and known either as Clausius's principle or the second law of thermodynamics. This principle is, that heat cannot pass of itself, or without compensation in the form of work done or of heat transferred in the opposite sense, from a colder to a hotter body. This principle is in conformity with our common experience, that heat passes by conduction or radiation from a place of higher to a place of lower temperature. It is not