The rod fits into a circular hole in a copper sheet with a clearance of 0.017 mm completely around it when both it and the sheet are at 18°C. (a) At what temperature will the clearance be zero? (b) Would such a tight fit be possible if the sheet were brass and the rod were copper?Explain. Also, can you please show your work.
Using A A0*(1 + 2*α*ΔT) we need ΔT where the area of each is the same so [A0*(1 + 2*α*ΔT)] brass [A0*(1 + 2*α*ΔT)] copper to simplify A π*r^2 so we can eliminate π from both sides leaving r^2 [0.70x10^-2m)^2*(1 + 2*2.0x10^-5*ΔT) (0.70x10^-2 + 0.017x10^-3)^2*(1 + 2*1.7x10^-5)*ΔT) Simplifying 4.9x10^-5 + 1.96x10^-9*ΔT 4.924x10^-5 + 1.674x10^-9ΔT So ΔT (4.924x10^-5 - 4.9x10^-5)/(1.96x10^-9 - 1.674x10^-9) 833oC So Tf 833 - 18 815oC b) If the metals were reversed then there could not be a tight fit because the brass plate would expand more rapidly that the copper rod so the clearance would become larger not smaller
