A liquid with a coefficient of volume expansion ' just fills a spherical shell of volume Vi at a temperature of Ti (see Fig. P19.47). The shell is made of a material that has an average coefficient of linear expansion &. The liquid is free to expand into an open capillary of area A projecting from the top of the sphere. (a) If the temperature increases by ΔT, show that the liquid rises in the capillary by the amount Δh given by Δh = (Vi/A)(B – 3a) ΔT. (b) For a typical system, such as a mercury thermometer, why is it a good approximation to neglect the expansion of the shell?