Question

Figure (28-E4) shows an aluminium rod joined to a copper rod. Each of the rods has a length of 20 cm and area of cross section 0.20 cm². The junction is maintained at a constant temperature 40°C and the two ends are maintained at 80°C. Calculate the amount of heat taken out from the cold junction in one minute after the steady state is reached. The conductivites are K_At = 200 W m⁻¹°C⁻¹ and K_Cu = 400 W m⁻¹°C⁻¹.

Answer 1

Area of cross section, A = 0.20 cm² = 0.2 × 10^–4 m²
Thermal conductivity of aluminium, K_Al = 200 W/​m ​°C
Thermal conductivity of copper, K_Cu = 400 W/m​°C
Total heat flowing per second = q_Al + q_Cu
$$\begin{gathered} =\frac{K_{\mathrm{Al}}\mathit{\times }A\mathit{\times }\left(80-40\right)}{l}+\frac{K_{\mathrm{Cu}}\times \mathrm{A}\times \left(80-40\right)}{l} \\ =\frac{200\times 0.2\times {10}^{-4}\times 40}{0.2}+\frac{400\times 0.2\times {10}^{-4}\times 40}{0.2} \\ =8\times {10}^{-1}+16\times {10}^{-1} \\ =24\times {10}^{-1} \\ =2.4\mathrm{J}/\sec \end{gathered}$$
Heat drawn in 1 minute = 2.4 × 60 = 144 J