It is desired to slip an aluminum ring over a steel bar (see Figure). At 10.00 °

Question

It is desired to slip an aluminum ring over a
steel bar (see Figure). At 10.00 °C the inside diameter of
the ring is 4.000 cm and the diameter of the rod is 4.040
cm. (a) Find the temperature of the ring at which it fits
over the bar. The bar remains at 10.0 °C. Once the
aluminum ring is slipped over the bar, the ring and bar
are allowed to equilibrate at a temperature of 22 °C. The
ring is now stuck on the bar.

(b) If the temperature of both the ring and the bar are changed together, should
the system be heated or cooled to remove the ring?

(c)Find the temperature at which the ring can be removed.

Please answer each part clearly and with all the variables defined

Explanation / Answer

(a) the ring should be heated for simplicity let us assume that the ringis cut and unrolled then it would be a rectangle if the rectangle is heated it would expandalong its length and width its length is the circumference of thering as the length of the rectangle increases thecircumference also increases and so does its diameter (b) Diameter of the ring do=4 cm Diameter of the steel rod d=4.04 cm Increase in length ?d=d- do=0.04 cm Temperature To=273+10=373 as L = C = p d ?L = ?C = p?d p ?d = a (pdo) ?T then the temperature will be T = To + (?d / ado) = 373+(0.04 / 2.4 x 10 -5*4) =789.6 K =789.6-273 = 516.6.oC C) system is cooled to remove AL ring from the steel rod d) then the temperature will be T = To- (?d / ado) = 373-0.04 / 2.4 x 10 -5*4) =-43.6 K =-43.6-273 = -316.6oC

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