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.
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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 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
TA
dt
JdT|
kA
dt
dQ
| dx
|AP|
|dx
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.
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