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A liquid with coefficient of volume expansion ? just fills a spherical container of volume V0...

A liquid with coefficient of volume expansion ? just fills a spherical container of volume V0 at temperature Ti (figure below). The flask is made of a material that has a coefficient of linear expansion of ?. The liquid is free to expand into a capillary of cross-sectional area A at the top. (a) Show that if the temperature increases by ?T, the liquid rises in the capillary by the amount ?h = (V0/A)(? ? 3?)?T. (Do this on paper. Your instructor may ask you to turn in this work.) (b) For a typical system, such as a mercury thermometer, why is it a good approximation to neglect the expansion of the flask?

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