Question

A cylinder of diameter 1cm at temp 30c is to be slid into a hole in steel plate.the hole had a diameter of 0.99970cm at temp 30c.To what temp must the plate be heated?

Answer 1

We can find to what temperature must the plate be heated from the thermal linear expansion formula:

$$\dfrac{\Delta L}{L_0}=\alpha \Delta T,$$ $$\Delta T=\dfrac{L-L_0}{\alpha L_0},$$ $$\Delta T=\dfrac{1\ cm-0.9997\ cm}{12\cdot10^{-6}\ ^{\circ}C^{-1}\cdot0.9997\ cm}=25^{\circ}.$$