Heat And Thermodynamics

A cylinder has a piston at temperature of \(30 \Upsilon\)C. There is all round clearance of \(0.08 \mathrm{~mm}\) between the piston and cylinder wall if internal diameter of the cylinder is \(15 \mathrm{~cm}\). What is the temperature at which piston will fit into the cylinder exactly?

\(\left(\alpha_p=1.6 \times 10^{-5} / \Upsilon\mathrm{C} \text { and } \alpha_c=1.2 \times 10^{-5} / \Upsilon\mathrm{C}\right)\)