A steel bolt is to be inserted through a circular hole in a brass plate

PHYSICS · Multi-part · CBSE · Physics · Thermal Properties of Matter · Thermal Properties of Matter

Problem

A steel bolt is to be inserted through a circular hole in a brass plate. At 20 ∘C20\,^{\circ}\text{C} the bolt diameter is 10.000 mm10.000\,\text{mm} while the hole diameter is 9.995 mm9.995\,\text{mm}. The assembly is heated uniformly until the bolt can just pass through the hole. Given: αsteel=1.2×10−5 K−1\alpha_{\text{steel}} = 1.2\times10^{-5}\,\text{K}^{-1}, αbrass=1.8×10−5 K−1\alpha_{\text{brass}} = 1.8\times10^{-5}\,\text{K}^{-1}. (i) Derive an expression for the temperature rise ΔT\Delta T required so that the hole becomes slightly larger than the bolt. (ii) Calculate the minimum temperature (in ∘C^{\circ}\text{C}) to which the bolt–plate system must be heated. (iii) If, instead of linear expansion coefficients, only the volumetric expansion coefficients of steel and brass were available, explain briefly how you would adapt your calculation in (i) and (ii).

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