Page:Elementary Text-book of Physics (Anthony, 1897).djvu/217

§ 177] and the temperature of the plane is $$t' - (t' - t)\frac{d'}{d}\cdot$$ The confirmation by experiment of this law of temperature distribution in a wall is a warrant for our assumption of the fundamental principle of the flow of heat.

176. Conductivity.—If, now, we consider a prism extending across the wall, bounded by planes perpendicular to the exposed surfaces, and represent the area of its exposed bases by $$A,$$ the quantity of heat which flows in a time $$T$$ through this prism may be represented by where $$K$$ is a constant depending upon the material of which the wall is composed. $$K$$ is the conductivity of the substance, and may be defined as the quantity of heat which in unit time flows through a section of unit area in a wall of the substance whose thickness is unity, when its exposed surfaces are maintained at a difference of temperature of one degree; or, in other words, it is the quantity of heat which in unit time flows through a section of unit area in a substance, where the rate of fall of temperature at that section is unity. In the above discussions the temperatures $$t'$$ and $$t$$ are taken as the actual temperatures of the surfaces of the wall. If the colder surface of the wall be exposed to air of temperature $$T,$$ to which the heat which traverses it is given up, $$t$$ will be greater than $$T.$$ The difference will depend upon the quantity of heat which flows, and upon the facility with which the surface parts with heat.

177. Flow of Heat along a Bar.—If a prism of a substance have one of its bases maintained at a temperature $$t,$$ while the other base and the sides are exposed to air at a lower temperature, the conditions of uniform fall of temperature no longer exist, and the amount of heat'which flows through the different sections is no longer the same: but the amount of heat which flows through any section is still proportional to the rate of fall of temperature at that