A brass plate with a thickness of 1.00 cm is placed over a copper plate with a thickness of 2.00 cm.The coefficient of thermal conductivity of brass is 100 W/m$^{\circ}$C and of copper is 400 W/m $^{\circ}$C.What is the effective coefficient of thermal conductivity for the brass-copper layer?

Question

Quizplus · Accepted Answer

The effective thermal conductivity for layers in series is given by the harmonic mean: $ k_{\text{eff}} = \frac{d_1 + d_2}{\frac{d_1}{k_1} + \frac{d_2}{k_2}} $. Substituting the given values, $ k_{\text{eff}} = \frac{0.01 + 0.02}{\frac{0.01}{100} + \frac{0.02}{400}} = 200 $ W/m°C.

A Brass Plate with a Thickness of 1 ∘^{\circ}∘ C and of Copper Is 400 W/m

A Brass Plate with a Thickness of 1 $^{\circ}$ C and of Copper Is 400 W/m