(Solved): The drawing shows a solid cylindrical rod made from a center cylinder of lead and an outer concentr ...

The drawing shows a solid cylindrical rod made from a center cylinder of lead and an outer concentric jacket of copper. Except for its ends, the rod is insulated (not shown), so that the loss of heat from the curved surface is negligible. When a temperature difference is maintained between its ends, this rod conducts \( 1 / 7 \) the amount of heat that it would conduct if it were solid copper. Determine the ratio of the \( \operatorname{radii~}_{1} / r_{2} \). Units A copper rod has a length of \( 1.5 \mathrm{~m} \) and a cross-sectional area of \( 4.0 \times 10^{-4} \mathrm{~m}^{2} \). One end of the rod is in contact with boiling water and the other with a mixture of ice and water. What is the mass of ice per second that melts? Assume that no heat is lost through the side surface of the rod. \[ \mathrm{m} / \mathrm{t}= \] Three building materials, plasterboard \( \left[k=0.30 \mathrm{~J} /\left(\mathrm{s} \mathrm{m} \mathrm{C}^{\circ}\right)\right] \), brick \( \left[k=0.60 \mathrm{~J} /\left(s \mathrm{~m} C^{\circ}\right)\right] \), and wood \( \left[k=0.10 \mathrm{~J} /\left(\mathrm{s} \mathrm{m} \mathrm{C}{ }^{\circ}\right)\right] \), are sandwiched together as the drawing illustrates. The temperatures at the inside and outside surfaces are \( 27.9^{\circ} \mathrm{C} \) and \( 0^{\circ} \mathrm{C} \), respectively. Each material has the same thickness and cross-sectional area. Find the temperature (a) at the plasterboard-brick interface and (b) at the brick-wood interface.