Consider a plane wall \(120 \mathrm{~mm}\) thick and of thermal conductivity \(120 \mathrm{~W} / \mathrm{m} \cdot \mathrm{K}\). Steady-state conditions are known to exist with \(T_{1}=500 \mathrm{~K}\) and \(T_{2}=700 \mathrm{~K}\). Determine the heat flux \(q_{x}^{\prime \prime}\) and the temperature gradient \(d T / d x\) for the coordinate systems shown.

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T(x) T (a) T T(x) T2 T2 T x (b) (c) T(x) T