Steel Delta
cooling a rivet to fit into a hole physic question?
Please help on the work, somehow i’m off by about 100 i think!
To make a secure fit, rivets that are larger than the rivet hole are often used and the rivet is cooled (usually by dry ice) before it is placed in the hole. A steel rivet 1.848cm in diameter is to be placed in a hole 1.846 cm in diameter. To what temp (C) must the rivet be cooled if it is to fit in the hole at 20 degrees C?
So i found At=pi(1.846cm)^2/4=2.676
A0=pi(1.848cm)^2/4=2.682
then to find delta t i did dt=(1-(At/A0)/11*10^-6 (coeff. for steel)=203
then took that number and subtracted from 20 and got -183deg C, but that is wrong because i know that the answer should be closer to the temp of the dry ice at around -80. what did i do wrong? Thank you!
∆L = α* Lo * ∆T —–> ∆L = 1.848 – 1.846 = 2 cm
coefficient of linear expansion for steel : α = 11 * 10^-6 oC^-1
—> ∆T = ∆L/α* Lo = 2/(11 * 10^-6 * 1848) = 98.39
—> T’ = T – ∆T ( it is cooled –>(-) sign)
= 20 – 98.39 = -78.39 ^oC
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