Gce Model Questions Vol1 2017 Physics Question 17

A copper rod (thermal conductivity \(k_{Cu}=400\ \text{W m}^{-1}\text{K}^{-1}\)) of length \(0.50\ \text{m}\) and cross‑sectional area \(1.0\times10^{-4}\ \text{m}^2\) is joined to an aluminium rod (thermal conductivity \(k_{Al}=205\ \text{W m}^{-1}\text{K}^{-1}\)) of length \(0.30\ \text{m}\) and the same cross‑section. The far ends of the copper and aluminium rods are kept at \(100^{\circ}\text{C}\) and \(20^{\circ}\text{C}\) respectively. The junction loses heat to the surroundings at \(25^{\circ}\text{C}\) by convection with heat‑transfer coefficient \(h = 10\ \text{W m}^{-2}\text{K}^{-1}\) over an area of \(0.020\ \text{m}^2\). Assuming steady‑state conditions, (a) calculate the rate of heat transfer through the system, and (b) determine the temperature at the junction.