A cylindrical aluminium can holds 500 cm ^3 of water, with the can's inner cross-sectional area being 125 cm ^2 . All these measurements are taken at 10^ C . Determine the rise in the water level when the temperature is raised to 80^ C . The coefficient of linear expansion of aluminium is 23 10⁻⁶ ^ C ⁻¹ and the average coefficient of volume expansion of water is 3.2 10⁻⁴ ^ C ⁻¹ .

Step-by-step solution

Initial volume of water, V₀ = 500 cm ³ Initial area of cross-section of the can, A₀ = 125 cm ² Initial height of the water level, h₀ = V₀ A₀ = 500 125 = 4 cm Change in temperature, T = 80^ C - 10^ C = 70^ C After the temperature is raised, the new volume of water is: V = V₀(1 + T) The new inner cross-sectional area of the aluminium can is: A = A₀(1 + 2 T) The new height of the water level is: h = V A = V₀(1 + T) A₀(1 + 2 T) = h₀ 1 + T 1 + 2 T Since 2 T 1 , using binomial approximation: h h₀(1 + T)(1 - 2 T) h₀(1 + (