A 771.0-kg copper bar is put into a smelter for melting.The initial temperature of the copper is 300.0 K.How much thermal energy 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 205,000 J/kg,and its melting point is 1357 K.

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Quizplus · Accepted Answer

To calculate the total thermal energy required to melt the copper bar, we need to consider both the energy required to raise the temperature of the copper to its melting point and the energy required to melt the copper at its melting point.1. Energy to raise the temperature to the melting point:$$Q_1 = mc\Delta T = (771.0\, \text{kg}) \times (386\, \text{J/kg}\cdot K) \times (1357\, K - 300\, K)$$$$Q_1 = 771.0 \times 386 \times 1057 = 314,205,402\, J$$2. Energy to melt the copper:$$Q_2 = m L_f = (771.0\, \text{kg}) \times (205,000\, \text{J/kg})$$$$Q_2 = 771.0 \times 205,000 = 158,055,000\, J$$Total energy required:$$Q_{\text{total}} = Q_1 + Q_2 = 314,205,402\, J + 158,055,000\, J = 472,260,402\, J$$$$Q_{\text{total}} = 4.72 \times 10^8\, J = 4.72 \times 10^5\, kJ$$Therefore, the closest answer is 4.73 × 10^5 kJ.

A 7710-Kg Copper Bar Is Put into a Smelter for Melting