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A liquid with a coefficient of volume expansion just fills a spherical shell of volume V (see figure below).

A liquid with a coefficient of volume expansion β just fills a spherical shell of volume V (see figure below). The shell and the open capillary of area A projecting from the top of the sphere are made of a material with an average coefficient of linear expansion α. The liquid is free to expand into the capillary. Assuming the temperature increases by ΔT, find the distance Δh the liquid rises in the capillary. (Use the following variables as necessary: A, alpha for α, beta for β, (DeltaT) for ΔT, and V.)

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