$[0/0\mathrm{.}66$ Points$]$ SERPSE$1018\mathrm{.}4.$OP$\mathrm{.}010.$CTX$.$

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You are working in a controlled environmental laboratory. For the experiments with which you are assisting, the temperature in the laboratory must stay fixed. Your supervisor has designed the sensitive mercury thermometer shown in the figure below. The graduated Pyrex glass capillary tube on the top has a diameter of $0\mathrm{.}00480$ cm and a length $l=3\mathrm{.}50cm,$ and the very thin Pyrex glass bulb has a diameter of $0\mathrm{.}200$ cm $.$ At the beginning of an experiment, the temperature in the laboratory is $24\mathrm{.}1C$ and the level of mercury is exactly at the bottom of the glass capillary as shown on the left in the figure below. Your supervisor asks you to determine the maximum temperature measurable by the thermometer $($in $C),$ that is$,$ the temperature at which mercury will reach the top of the capillary tube as shown on the right in the figure below. Because of the very small volume of the capillary tube compared to that of the glass sphere, you can ignore its expansion as the temperature changes.

The difference in the expanded volumes of the mercury and the glass equals the volume of mercury in the capillary. $C$