A close analogy exists between the flow of energy by heat because of a temperature difference (see Section 20.7) 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 electrical conductor is usually a good thermal conductor as well. Consider a thin conducting slab of thickness dx, area A, and electrical conductivity o, 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 dQ TA dt | dx |AP| kA dt | dx |LP| In the analogous thermal conduction equation on the right (Eq. 20.15), the rate dQ/dt of energy flow by heat (in Sl units of joules per second) is due to a temperature gradient dT/dx in a material of thermal conductivity k (b) State analogous 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.

A close analogy exists between the flow of energy by heat because of a temperature difference (see Section 20.7) 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 electrical conductor is usually a good thermal conductor as well. Consider a thin conducting slab of thickness dx, area A, and electrical conductivity o, 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 dQ TA dt | dx |AP| kA dt | dx |LP| In the analogous thermal conduction equation on the right (Eq. 20.15), the rate dQ/dt of energy flow by heat (in Sl units of joules per second) is due to a temperature gradient dT/dx in a material of thermal conductivity k (b) State analogous 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.