A liquid with a coefficient of volume expansion of b just fills a spherical flask of volume V0 at temperature T (Fig. P10.57). The flask is made of a material that has a coefficient of linear expansion of a. 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)(β - 3α) ?T. (b) For a typical system, such as a mercury thermometer, why is it a good approximation to neglect the expansion of the flask?FIGURE P10.57

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