Question

11. (10 pts) A glass beaker with volume 1 liter is completely filled with water at 20°C. How much water will spill out of the glass beaker when the temperature is raised to 90°C? Use the table below if needed (α and β are the coefficients of linear expansion and volume expansion, respectively. Approximate Coefficients of Thermal Expansion at 20oC a (10-"/oc) 23 12 Material Aluminum Concrete Diamond Glass Stainless Steel Water B (10°/oc) 69 36 3 27 51 207 9 17 69 *(Note) Water actually expands when it freezes, so calculations near the freezing point of water (between 0°C and 4°C) require a different analysis.

Answer 1

Formula for volume expansion is give by delta V = V (1 + B delta T) where V is volume at initial temperature B rightarrow coefficient of volume expansion here for glass beta_1 = 27 times 10^-6/degree c V_1 = 1 liter so delta V_1 = v_1 (1 + beta_1 delta T) = 1 [1 + 27 times 10^-6 times (90 - 20)] delta V_1 = 1 + 27 times 70 times 10^-6 liter for water beta_2 = 207 times 10^-6/degree c v_2 = 1 liter so delta v_2 = V_2 (1 + beta_2 delta T) = > delta v_2 = 1 [1 + 207 times 10^-6 times (90-20)] = > delta v_2 = 1 + 207 times 70 times 10^-6 liter amount of water spill out of glass = delta V_2 - delta v_1 = 1 + 207 times 10^-6 times 70 - 1 - 27 times 106-6 times 70 = 180 times 70 times 10^-6 = 0.126 liter hence 0.126 liter or 128 ml will spill out of the glass