A copper rod 2 m long has a circular cross-section of radius 1 cm. One end is kept at `100^@C` and the other at `0^@C`. The surface is insulated so that negligible heat is lost through the surface. In steady state, find
(a) the thermal resistance of the bar
(b) the thermal current H
(c) the temperature gradient `(dT)/(dx)` and
(d) the temperature at a distance 25 cm from the hot end.
Thermal conductivity of copper is 401 `W//m-K.`

Answer

A, B, C, D

Explanation

(a) Thermal resistance, `R = l/(KA) = l/(K(pir^2))`
or `R=((2)/((401)(pi)(10^-2)^2))`
`= 15.9 K//W`
(b) Thermal current, `H = (DeltaT)/R = (Deltatheta)/R = (100)/(15.9)`
or `H=6.3 W`
(c) Temperature gradient
`=(0-100)/2 = -50K//m`
`=-50^@C//m`
(d) Let `theta` be the temperature at 25 cm from the hot end, then

`(theta -100) = ("temperature gradient") xx ("distance")`
or `theta- 100 = (-50)(0.25)`
or `theta = 87.5^@C` .