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A spherical steel ball bearing has a diameter of 2.540 cm at 26.00°C. (Assume the coefficient of linear expansion of the steel is 1.10 10-5(°C-1), and the average volume expansion coefficient is 3.30 10-5(°C-1).)A) What is its diameter when its temperature is raised to 97.0°C? (Give your answer to four significant figures in cm.)B) What temperature change is required to increase its volume by 1.100%?

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Answer:

a) 2.542 cm

b) 30.30 °C

Explanation:

a) Δd = coefficient of linear expansion x original diameter x change in

            temperature

         = αdΔT

         = 1.10 x 10^-5 x 2.54 x (97 - 26)

         = 0.00198374 cm

new diameter = 2.540 cm + 0.00198374 cm = 2.54198374 cm = 2.542 cm

b) change in volume = average volume expansion coefficient x original

                                      volume x change in temperature

                              ΔV = βVΔT

                       0.0011V = 3.30 x 10^-5 x V x ΔT

                                 ΔT = 30.30 °C

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