Page:Reflections on the Motive Power of Heat.djvu/116

94 shown the relation between these temperatures and the quantities of motive power produced. It would at first seem natural enough to suppose that for equal differences of temperature the quantities of motive power produced are equal; that is, for example, the passage of a given quantity of caloric from a body, A, maintained at 100°, to a body, B, maintained at 50°, should give rise to a quantity of motive power equal to that which would be developed by the transfer of the same caloric from a body, B, at 50°, to a body, C, at zero. Such a law would doubtless be very remarkable, but we do not see sufficient reason for admitting it à priori. We will investigate its reality by exact reasoning.

Let us imagine that the operations described on p. 70 be conducted successively on two quantities of atmospheric air equal in weight and volume, but taken at different temperatures. Let us suppose, further, the differences of temperature between the bodies A and B equal, so these bodies would have for example, in one of these cases, the temperatures 100° and 100° − h (h being indefinitely small), and in the other 1° and 1° − h. The quantity of motive power produced is, in each case, the difference between that which the gas supplies by its dilatation and that which must be expended to restore its primitive volume. Now this