You are designing a precision mercury thermometer based on the thermal expansion of mercury (?=1.81?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 ?V=?V0?T, where V0 is the initial volume of the mercury and ?V is the change in volume due to a change in temperature, ?T. In response to a temperature change of 1.00°C, the column of mercury in your precision thermometer should move a distance D=1.33cm up a cylindrical capillary of radius r=0.133mm.
a) Determine the initial volume of mercury that allows this change.
b) Find the radius of a spherical bulb that contains this volume of mercury.