Two thermal reservoirs are connected by a solid copper bar. The bar is 3 m long, and the temperatures of the reservoirs are 63.0°C and 32.0°C. (The thermal conductivity of copper is 386 W/(m K).)
(a) Suppose the bar has a constant rectangular cross section, 10 cm on a side. What is the rate of heat flow through the bar?
(b) Suppose the bar has a rectangular cross section that gradually widens from the colder reservoir to the warmer reservoir. The area A is determined by
A = (0.010 m2)[1.0 + x/(3.0 m)],
where x is the distance along the bar from the colder reservoir to the warmer one. Find the (rate of) heat flow.
(c) Find the rate of change of temperature in °C/m with distance at the colder end, at the warmer end, and at the middle of the bar.