12 13 (a) If the diameter of a aluminum sphere is 2.540 cm at 26.60 If the diame

Question

12  13

(a) If the diameter of a aluminum sphere is 2.540 cm at 26.60

If the diameter of a aluminum sphere is 2.540 cm at 26.60degreeC, what will its diameter be at a temperature of 106.0degreeC? The coefficient of linear expansion of aluminum is 25 ? 10-6/degreeC. (Give your answer to at least three decimal places.) For the volume of the sphere to increase by 1.160%, to what temperature should the sphere be heated? The coefficient of volume expansion is 3 times that of linear expansion for the metal. What is the equation describing the volume expansion due to temperature changes? degreeC

Explanation / Answer

alpha = change in diameter / ( initial diameter x change in temperature )

25 x 10-6 = change in diameter / 2.540 x 79.4

change in diameter = 25 x 10-6 x 2.540 x 79.4

change in diameter = 5.0419 x 10-3

final diameter = 2.540 + 5.0419 x 10-3

final diameter =2.5450419

so the final diameter is 2.5450419 cm

2) gamma = change in volume / ( initial volume x change in temp)

given gamma = 3 x alpha = 75 x 10-6

75 x 10-6 = 0.0116 v / ( v x change in temp )

change in temp = 154.66

final temp = 154.66 + 26.60

final temp = 181.26 C

So the final temperature is 181.26 C

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