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A metallic sphere of radius 5 cm is concentric with a hollow metallic sphere of radius 20 cm, and the gap is filled with a non-metal. The inner and outer surfaces are held at 50 deg C and 10 deg C, and 100 J of heat flows outward each second. Find the thermal conductivity of the filling material.

1. 3.0 W/m-deg C
2. 4.0 W/m-deg C
3. 5.0 W/m-deg C
4. 6.0 W/m-deg C

Correct answer: 3.0 W/m-deg C

Solution

Solving Q = 4*pi*k*r1*r2*dT/(r2-r1) for k gives k = 100*0.15/(4*pi*0.01*40) ~ 3.0 W/m-deg C.

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