You are designing a precision mercury thermometer based on the thermal expansion of mercury (β = 1.8 ∙ 10–4 °C–1 ), which causes the mercury to expand up a thin capillary as the temperature increases. The equation for the change in volume of the mercury as a function of temperature is Δ V = β V 0 Δ T, where V 0 is the initial volume of the mercury and Δ V is the change in volume due to a change in temperature, Δ T. In response to a temperature change of 1.0 °C, the column of mercury in your precision thermometer should move a distance D = 1.0 cm up a cylindrical capillary of radius r = 0.10 mm. Determine the initial volume of mercury that allows this change. Then find the radius of a spherical bulb that contains this volume of mercury.
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