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Chapter 3: Q100P (page 580)

One experimental method of measuring an insulating material鈥檚 thermal conductivity is to construct a box of the material and measure the power input to an electric heater inside the box that maintains the interior at a measured temperature above the outside surface. Suppose that in such an apparatus a power input of 180Wis required to keep the interior surface of the box(about120F掳) above the temperature of the outer surface. The total area of the box is2.18m2, and the wall thickness is 3.90cm. Find the thermal conductivity of the material in SI units.

Short Answer

Expert verified

The thermal conductivity of the material in SI units is0.05W/m.K.

Step by step solution

01

Definition of the heat current

The heat current in conduction is,

H=dQdt=kATH-TcL

Here, k is the thermal conductivity of rod material, A is the cross-sectional area of the rod, and TH-TCLis the temperature difference per unit length, called temperature gradient.

02

Calculation of the thermal conductivity of the material in SI units

Given that the change in temperature is TH-Tc=65C掳, the power is H = 180W , the cross-sectional area of the box isA=2.18m2, and the thickness of the box is.

L=3.9脳10-2m

The thermal conductivity of the material from the heat current in conduction is,

k=HLATH-Tc

Substitute all the known values in the above equation to find the thermal conductivity.

k=180W脳3.9脳10-2m2.18m2脳65掳C=0.05W/m.C掳=0.05W/m.K

Hence, the thermal conductivity of the material in SI units is 0.05W/m.K.

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