Phase changes: A 406.0 kg copper bar is put into a smelter for melting. The initial temperature of the copper is 300.0 K. How much heat must the smelter produce to completely melt the copper bar? (The specific heat for copper is 386 J/kg ∙ K, the heat of fusion for copper is 205 kJ/kg, and its melting point is 1357 K.) A) 2.49 × 10⁵_kJ B) 1.66 × 10¹¹_kJ C) 1.66 × 10⁸_kJ D) 2.96 × 10⁵_kJ

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Quizplus · Accepted Answer

The correct answer is A because the heat required to melt the copper bar is the sum of the heat required to raise the temperature of the copper from 300.0 K to its melting point of 1357 K and the heat required to melt the copper at its melting point. The heat required to raise the temperature of the copper is given by:Q1 = m * c * (Tf - Ti)where m is the mass of the copper bar, c is the specific heat of copper, Tf is the melting point of copper, and Ti is the initial temperature of the copper.Q1 = (406.0 kg) * (386 J/kg ∙ K) * (1357 K - 300.0 K) = 2.01 × 10^8 JThe heat required to melt the copper at its melting point is given by:Q2 = m * Lfwhere Lf is the heat of fusion of copper.Q2 = (406.0 kg) * (205 kJ/kg) = 8.32 × 10^7 JTherefore, the total heat required to melt the copper bar is:Q = Q1 + Q2 = 2.01 × 10^8 J + 8.32 × 10^7 J = 2.84 × 10^8 JConverting to kJ, we get:Q = 2.84 × 10^8 J * (1 kJ/1000 J) = 2.84 × 10^5 kJTherefore, the smelter must produce 2.84 × 10^5 kJ of heat to completely melt the copper bar.

Phase Changes: a 406