Question

A copper flask is filled to the brim with mercury. Both the flask and the mercury are at an initial temperature of 20.0°C. After they are heated to a temperature of 78.0°C, 12.6 cm3 of mercury spills out. What was the initial volume of the flask? Give your answer in BOTH cm3 and m3

Answer 1

Let co-efficient of volume expansion of copper = 5.1 times 10^-5/ degree C coefficient of volume expansion of Mercury = 18 times 10^-5/ degree c here flask is filled upto brines with mercury and due to heating copper & Hg will expand So we have to consider expansions of both let r_app = r_Real - r_c r_app = Apparent co efficient of expansion /degreeC r_Real = Real coefficient expansion of Hg /degreeC r_c = coefficient of expansion of container /degreeC So by Heating volume expansion or change in volume is given by equation Av = v_0 r_app middot AT A_v = increase in volume m^3 v_0 = original volume of container, m^3 Delta T = increase in temperature degree C = 78 - 20 = 58 degree Delta v = 12.6 cm^3 12.6 = v_0 times (18 times 10^-5 - 5.1 times 10^-5) times 58 v_0 = 12.6/58 times 10^5 (18 - 5.1) = 12.6/.00748 v_0 = 1684.49 cm^3