City Guilds Model Questions Vol1 2023 Engineering Question 35

A steel component (0.8 % C, 0.3 % Mn, 0.2 % Cr) must attain a hardness of 55 HRC after heat treatment. The hardness after tempering is given by \(H = H_{\text{max}} - \alpha \log_{10}(t)\) where \(H_{\text{max}} = 60\) HRC, \(\alpha = 2.5\), and \(t\) is the tempering time in minutes. Determine the tempering time required (to the nearest minute) to achieve the target hardness. Then, using the tempering‑time relation \(t = k\,\exp\!\left(\frac{Q}{R T}\right)\) with \(k = 1\times10^{-6}\ \text{min}\), \(Q = 200\,\text{kJ\,mol}^{-1}\) and \(R = 8.314\ \text{J\,mol}^{-1}\!\!\,\text{K}^{-1}\), calculate the tempering temperature \(T\) (in °C) that would give this time. Provide the tempering time and the corresponding temperature.