A hot reservoir is maintained at a temperature of 56 o C, and a cold reservoir i

Question

A hot reservoir is maintained at a temperature of 56 oC, and a cold reservoir is maintained at a temperature of 16oC. They are separated by 12.00 cm, and are connected by a cylindrical bar made of two materials. The radius of the bar is 0.83 cm. The upper part of the bar is made of aluminum (k = 237 W/(moC)), and has a length of 3.00 cm. The lower part's material is unknown. The temperature where the two materials are in thermal contact is 50.4310 oC. What is the rate of heat flow through the bar?

Find the thermal conductivity of the unknown substance. (In W/m/degC.)

Explanation / Answer

Let T be the temperature at the interface=50.431

as heat transfer rate has to be constant

heat transfer rate through unknown substance = heat transfer through aluminium =237 x 3.141 x (0.83 x 10^-2)^2 (56-50.431)/ 3x 10^-2 = 10.33 W

b. now k x 3.141 x (0.83x 10^-2)^2(50.431- 16)/9x 10^-2 = 10.33

k= 12.48 W/m/degC

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