When the temperature of mercury changes by ΔT, the fractional volume change, ΔV/V, is given by ΔV/V = βΔT, where β = 1.8 10-4 K-1 is the coefficient of thermal expansion. Consider a thermometer containing a bulb attached to a thin, cylindrical capillary tube. If the bulb and capillary tube contain 0.3 cm3 of mercury, how large must the diameter of the capillary tube be so that a 4 K change in temperature corresponds to a 1 mm change in the mercury level in the capillary tube? (Neglect the change in volume of the glass bulb when the temperature is raised by 4 K.)
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