A cylinder has a piston at temperature of 30 ° C . There is all round clearance of 0 . 08   mm…

For the piston to get fit exactly into the cylinder, the thermal expansion of the piston should be $0.08 \mathrm{mm}$from both sides along the diameter of piston, therefore, total clearance should be $\delta =2\times 0.08 \mathrm{mm}=0.16 \mathrm{mm}$

Now, using the formula for linear expansion due to temperature $\delta =\alpha ∆TL$ Here, $L$is the length of internal diameter of the cylinder, $L=15 \mathrm{cm}=150 \mathrm{mm}$

$$\begin{gathered} \Rightarrow 0.16 \mathrm{mm}=\left({\mathrm{\alpha }}_{\mathrm{p}}-{\mathrm{\alpha }}_{\mathrm{c}}\right)∆T\left(150 \mathrm{mm}\right) \\ \Rightarrow ∆T=\frac{0.16}{150\times \left(1.6-1.2\right)\times {10}^{-5}}=268°\mathrm{C} \\ \Rightarrow T_{\mathrm{C}}-T_{\mathrm{p}}=268°\mathrm{C} \cdots \cdots \left(T_{\mathrm{p}}=30°\mathrm{C}\right) \\ \Rightarrow T_{\mathrm{C}}=T_{\mathrm{p}}+268°\mathrm{C}=298°\mathrm{C} \end{gathered}$$