A long rod, insulated to prevent heat loss along its sides, is in perfect thermal contact with boiling water (at atmospheric pressure) at one end and with an ice-water mixture at the other . The rod consists of a 1.00\;{\rm m} section of copper (with one end in the boiling water) joined end-to-end to a length L_2 of steel (with one end in the ice water). Both sections of the rod have cross-sectional areas of 4.00 {\rm cm^{2}}. The temperature of the copper-steel junction is 65.0{\rm ^{\circ} C} after a steady state has been reached. Assume that the thermal conductivities of copper and steel are given by k_{\rm copper}=385\;{\rm \frac{W}{m \cdot K}} and k_{\rm steel}=50.2\;{\rm \frac {W}{m \cdot K}}.

What is the length L_2 of the steel section?


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