A microwelding process uses a laser to weld two stainless steel micro$-$wires, each with a diameter of $\backslash (\backslash$mathbf$\{100\}\backslash$boldsymbol$\{\backslash$mu m$\}\backslash ).$ The laser operates with a power of $\backslash (\backslash$mathbf$\{0.5\}\backslash$mathbf$\{$W$\}\backslash )$ for $\backslash (\backslash$mathbf$\{5\}\backslash )$ seconds. The specific heat capacity of stainless steel is $\backslash (\backslash$mathbf$\{500\}\backslash$mathbf$\{$J$\}/\backslash$mathbf$\{$k g$\}\backslash$cdot $\backslash$mathbf$\{$K$\}\backslash ),$ and its density is $\backslash (\backslash$mathbf$\{8000\}\backslash$mathbf$\{$~ k g$\}/\backslash$mathbf$\{$m$\}^\{\backslash$mathbf$\{3\}\}\backslash ).$ The process is $\backslash (50\backslash \%\backslash )$ efficient in converting laser energy into heat for welding.

Assume the weld area is a circular cross$-$section with a diameter equal to the wire diameter, and the temperature of the micro$-$wires rises from room temperature $(\backslash (\backslash$mathbf$\{300\}\backslash$mathbf$\{$~ K$\}\backslash ))$ to $\backslash (\backslash$mathbf$\{1500\}\backslash$mathbf$\{$K$\}\backslash )$ during the welding process.

After welding, the micro$-$joint is subjected to a tensile test. The joint has a cross$-$sectional area of $\backslash (\backslash$mathbf$\{0.01\}\backslash$mathbf$\{$m m$\}^\{\backslash$mathbf$\{2\}\}\backslash )$ and breaks under a load of $\backslash (\backslash$mathbf$\{70\}\backslash$mathbf$\{$N$\}\backslash ).$

$1.$ Calculate the total heat energy absorbed by the micro$-$wires during the welding process.

$2.$ Estimate the temperature rise in the micro$-$wires based on the heat absorbed$.$

$3.$ Calculate the tensile strength of the micro$-$weld joint.