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 electrical conductor is usually a good thermal conductor as well. Consider a thin conducting slab of thickness dx, area A, and electrical conductivity a, with a potential difference dVbetween opposite faces. (a) Show that the current I= dq/dt is given by the equation on the left: Charge conduction Thermal conduction |av GA dx dq dQ = kA dt dt 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 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 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 electrical conductor is usually a good thermal conductor as well. Consider a thin conducting slab of thickness dx, area A, and electrical conductivity a, with a potential difference dVbetween opposite faces. (a) Show that the current I= dq/dt is given by the equation on the left: Charge conduction Thermal conduction |av GA dx dq dQ = kA dt dt 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 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.
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Transcribed Image Text: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 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 dVbetween opposite faces. (a) Show that the
current I= dq| dt is given by the equation on the left:
Charge conduction Thermal conduction
da
= GA
dt
dQ
= kA
dx
dt
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 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.
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