An iron cube (density = 8000 kg m ⁻³ , specific heat capacity = 470 J kg ⁻¹ K ⁻¹ ) is raised to a high temperature and placed upon a large block of ice at 0^ C . The cube melts the ice beneath it, displaces the resulting water, and sinks. At the final equilibrium position, the upper surface of the cube just aligns with the surface of the ice. Determine the initial temperature of the cube. Neglect any heat loss outsid

Step-by-step solution

Let the volume of the iron cube be V . Since the upper surface of the cube just aligns with the surface of the ice at the final equilibrium position, the volume of the ice melted is exactly equal to the volume of the cube. Mass of the ice melted is given by: m_ ice = _ ice V The heat required to melt this amount of ice is: Q = m_ ice L_f = _ ice V L_f The heat released by the iron cube as it cools from its initial temperature T to 0^ C is: Q = m_ Fe c_ Fe T = _ Fe V c_ Fe T By the principle of calorimetry, assuming