Question

A spherical steel ball bearing has a diameter of 2.540 cm
at 25°C. (a) What is its diameter when its temperature is
raised to 100°C? (b) What temperature change is required
to increase its volume by 1%?

Answer 1

here constants are not given, so they are taken as coefficient of linear expansion of steel= 1*10^-5 and coefficient of volume expansion of steel= 3*10^-5 .

so, diameter at 100°C is given by the relation diameter at 25°C * ( 1+ coefficient of linear expansion of steel*temperature change ) = 2.54*(1+10^-5*(100-25)) = 2.541905 cm

similarly, for temperature change required to increase its volume by 1% , 1.01 V = V * ( 1 + 3*10^-5*t )

so, t= 333.33 °C

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