A spherical steel ball bearing has a diameter of 2.540 cm at 21.00 A spherical s

Question

A spherical steel ball bearing has a diameter of 2.540 cm at 21.00

A spherical steel ball bearing has a diameter of 2.540 cm at 21.00 degree C. (Assume the coefficient of linear expansion of the steel is 1.10 10-5(degreeC?1), and the average volume expansion coefficient is 3.30 10-5(degree C?1).) What is its diameter when its temperature is raised to 109.0 degree C? (Give your answer to four significant figures.) in centimeteres What temperature change is required to increase its volume by 0.800%? in celsius

Explanation / Answer

d 2 = d1( 1 + ?t)
t = 109-21 = 88
d 2 = 2.540*( 1 + 1.1e-5*88) = 2.54246 cm
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V2 = V1 + V1?t
It is given that (V1 ?t) /V1 = 0.800%= 0.008
?t = 0.008
t = 0.008 / 3.3e-5 = 242.42

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