Page:Elementary Text-book of Physics (Anthony, 1897).djvu/216

202 rapidly falls to the freezing-point, while the great mass of the water remains at the temperature of its maximum density.

174. Conduction.—If one end of a metal rod be heated, it is found that the heat travels along the rod, since those portions at a distance from the source of heat finally become warm. This process of transfer of heat from molecule to molecule of a body, while the molecules themselves retain their relative places, is called conduction.

In the discussion of the transfer of heat by conduction it is assumed as a principle, borne out by experiment, that the flow of heat between two very near parallel planes, drawn in a substance, is proportional to the difference of temperature between those planes, or that the flow of heat across a plane is proportional to the rate of fall of temperature across that plane.

175. Flow of Heat across a Wall.—The simplest body in which the flow of heat can be studied is a wall of homogeneous material bounded by two parallel infinite planes, one of which is kept at the temperature $$t'$$ and the other at the temperature $$t;$$ we represent the distance between the planes or the thickness of the wall by $$d.$$ We suppose that the flow of heat across this wall has continued so long that it has become steady, or that the temperatures at all points have assumed flnal values. Manifestly the temperature at all points in any plane parallel with the faces of the wall is the same, and the same amount of heat passes across any one such plane as passes across any other. We conclude therefore by the fundamental principle assumed (§ 174) that the rate of change of temperature across each plane in the wall is the same, or that the change of temperature throughout the wall from one face to the other is uniform; the rate of change of temperature is therefore given by $$\frac{t' - t}{d},$$ where it has been assumed that $$t'$$ is the higher temperature. If $$d'$$ represent the distance of any plane in the wall from the hotter surface, the fall of temperature between it and the hotter surface is $$(t' - t)\frac{d'}{d},$$