Two long copper rods of diameter \(D=8 \mathrm{~mm}\) are soldered together end to end, with solder having a melting point of \(250^{\circ} \mathrm{C}\). The rods are in air at \(30^{\circ} \mathrm{C}\) with a convection coefficient of \(10 \mathrm{~W} / \mathrm{m}^{2} \cdot \mathrm{K}\). What is the minimum power input needed to effect the soldering?