Question

1 Thermal Expansion A steel rod is 3.000 cm in diameter at 25 °C. A brass ring has an inner diameter of 2.902 ㎝ at 25。C. At what common tempernture will the ring just fit outo the srod? o c The coefficient of linear expansion of brass is 19.10-6 per °c.

PLEASE SHOW ALL YOUR WORK AND EXPLAIN YOUR STEPS. THANK YOU!

Answer 1

αS = 11 x 10-6 /Co

and

αBr = 19 x 10-6 /Co

They will have the same diameter when

DS = (3.000 cm)

DBr = (2.992 cm)

DS = (3.000 cm)(1 + α S∆T) = DBr = (2.992 cm)(1 + α Br∆T)

(3.000 - 2.992)cm = [(2.992 cm)αBr - (3.000 cm)αS]∆T = 0.008 cm = ∆T(56.848 - 33) x 10-6 cm/Co

∆T = (0.008/(23.848 x 10-6)]Co = 335.5 Co

-> T = (25 + 335)oC = 360oC