A close analogy exists between the flow of energy by heat because of a temperature difference (see Section 19.6) and the flow of electric charge because of a potential difference. In a metal, energy dQ and electrical charge dq are both transported by free electrons. Consequently, a good electri- cal conductor is usually a good thermal conductor as well. Consider a thin conducting slab of thickness dx, area A, and electrical conductivity ơ, with a potential difference dV between opposite faces. (a) Show that the current I = dq/dt is given by the equation on the left: Charge conduction Thermal conduction dq = oA dt dT kA dt dQ AP dx dx In the analogous thermal conduction equation on the right (Eq. 19.17), the rate dQ/dt of energy flow by heat (in SI units of joules per second) is due to a temperature gradient dT/dx in a material of thermal conductivity k. (b) State anal- ogous rules relating the direction of the electric current to the change in potential and relating the direction of energy flow to the change in temperature. dT P = kA dx (19.17)

A close analogy exists between the flow of energy by heat because of a temperature difference (see Section 19.6) and the flow of electric charge because of a potential difference. In a metal, energy dQ and electrical charge dq are both transported by free electrons. Consequently, a good electri- cal conductor is usually a good thermal conductor as well. Consider a thin conducting slab of thickness dx, area A, and electrical conductivity ơ, with a potential difference dV between opposite faces. (a) Show that the current I = dq/dt is given by the equation on the left: Charge conduction Thermal conduction dq = oA dt dT kA dt dQ AP dx dx In the analogous thermal conduction equation on the right (Eq. 19.17), the rate dQ/dt of energy flow by heat (in SI units of joules per second) is due to a temperature gradient dT/dx in a material of thermal conductivity k. (b) State anal- ogous rules relating the direction of the electric current to the change in potential and relating the direction of energy flow to the change in temperature. dT P = kA dx (19.17)

College Physics

11th Edition

ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

Section: Chapter Questions

Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...

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