A well-insulated uniform rod of cross section 1 cm2 and length 3d = 30 cm has te

Question

A well-insulated uniform rod of cross section 1 cm2 and length 3d = 30 cm has temperature probes attached at positions d = 10 cm and 2d = 20 cm as illustrated. A 16-watt heating element is attached at the left end. The rod and the heat sink at the right end are initially at a temperature of zero °C. After the heating element is switched on (and held on), the temperatures at the two positions increase and approach, after a long time, values of T1= 32°C and T2 = 16°C.
What is the thermal conductivity of the material of the rod?

(a) 235 watt m-1 K-1
(b) 401 watt m-1 K-1
(c) 1000 watt m-1 K-1

Explanation / Answer

use the conduction equation

   power = k A deltaT / x

   16 = k * 0.0001 * 16 / 0.10

k = 1000 W/m-K

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