A cylinder has a piston at temperature of 30 ° C . There is all round clearance of 0 . 08 mm between the piston and cylinder wall if internal diameter of the cylinder is 15 cm . What is the temperature at which piston will fit into the cylinder exactly? α p = 1 . 6 × 10 - 5 / C ∘ and α c = 1 . 2 × 10 - 5 / C ∘

Step-by-step solution

For the piston to get fit exactly into the cylinder, the thermal expansion of the piston should be 0 . 08   mm   from both sides along the diameter of piston, therefore, total clearance should be δ = 2 × 0 . 08   mm = 0 . 16   mm Now, using the formula for linear expansion due to temperature δ = α ∆ T L Here, L   is the length of internal diameter of the cylinder, L = 15   cm = 150   mm ⇒ 0 . 16   mm = α p - α c ∆ T 150   m