(Solved): 2. Fourier's law for heat conduction says that the energy flow rate across area A driven by a t ...

2. Fourier's law for heat conduction says that the energy flow rate across area $A$ driven by a temperature gradient $\mathrm{d}T/\mathrm{d}x$ for a material of thermal conductivity $?$ is given by $\frac{\mathrm{d}Q}{\mathrm{d}t}=??A\frac{\mathrm{d}T}{\mathrm{d}x}$ A long rod has a uniform cross-sectional area of $4.0{\mathrm{cm}}^2$. It is made of two sections joined end-to-end: a $75.0\mathrm{cm}$ long section of copper, and a $25.0\mathrm{cm}$ section of steel. The rod is insulated to prevent heat loss along its sides. The copper end is placed in perfect thermal contact with boiling water at $100^{?}\mathrm{C}$ and the steel end is placed in perfect thermal contact with an ice-water mixture at $0^{?}\mathrm{C}$. The thermal conductivities of copper and steel are $385.0\mathrm{W}{\mathrm{m}}^{?1}{\mathrm{K}}^{?1}$ and $50.2\mathrm{W}{\mathrm{m}}^{?1}{\mathrm{K}}^{?1}$ respectively. (a) Draw a sketch graph to show how the temperature varies along the rod in the steady state. $[4]$ (b) What is the temperature of the copper-steel junction in the steady state? $[6]$ (c) What is the rate of heat transfer from the steam bath to the ice-water mixture in the steady state? [ 4 ] (d) What is the rate of entropy production? $[4]$ (e) What would be the junction temperature, heat flow and entropy creation rate if the cross-sectional area of the rod were doubled? [ 2 ]