A steel bar 10 centimeters long is welded end to end to a copper bar 20 centimeters long. Each bar has a cross sectional area of 4 square centimeters. The free end of the steel bar is in contact with steam at 100 oC, and the free end of the copper bar is in contact with ice at 0 oC. Find the temperature at the junction of the two bars.I just need help on how to find the answer! I don‘t need the actual answer. Thank you! :)
Use Fourier's law for each segment and continuity of heat low: j1 A kappa_1 * A * delta(T1) *delta(L1) j2 A kappa_2 * A * delta(T2)*delta(L2) kappa1 is the thermal conductivity for steel, delta T1 the temp difference between its ends et cetera. let T be the temp at the junction, then kappa1 ( 373 - T) / L1 kappa2 (T-273) / L2 Solve for T.
Use the heat conduction equation (see link) Call the temperatire at the junction T. Call the thermal conductivity of steel ks, and copper kc. You should be given these values, otherwise you have to look them up. For the steel, the rate of heat transfer along the rod is ks.A(100-T)/0.1 For the copper the rate of heat transfer along the rod is kc.A(T-0)/0.2 Assuming the sides are insulated heat enters and leaves only at the ends, so ks.A(100-T)/0.1 kc.A(T-0)/0.2 Cross sectional area, A cancels, so the value is not needed. ks(100-T)/0.1 kcT/0.2 100ks- ksT 0.5kcT 0.5kcT + ksT 100ks T(0.5kc + ks) 100ks T 100ks / (0.5kc + ks)
