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 heat must the smelter produce to completely melt the copper bar? The specific heat for copper is $386 \mathrm {~J} / \mathrm { kg } \cdot \mathrm { K }$ the heat of fusion for copper is 205,000 J/kg, and its melting point is 1357 K.

Question

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 heat must the smelter produce to completely melt the copper bar? The specific heat for copper is $386 \mathrm {~J} / \mathrm { kg } \cdot \mathrm { K }$ the heat of fusion for copper is  205,000 J/kg, and its melting point is  1357 K.

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 1357 K and the heat required to melt the copper at 1357 K. The heat required to raise the temperature of the copper is:$$Q_1 = mc_p(T_f - T_i) = (771.0 \mathrm{~kg})(386 \mathrm{~J} / \mathrm{~kg} \cdot \mathrm{~K})(1357 \mathrm{~K} - 300.0 \mathrm{~K}) = 3.15 	imes 10^8 \mathrm{~J}$$The heat required to melt the copper is:$$Q_2 = mL = (771.0 \mathrm{~kg})(205,000 \mathrm{~J} / \mathrm{~kg}) = 1.58 	imes 10^8 \mathrm{~J}$$Therefore, the total heat required to melt the copper bar is:$$Q = Q_1 + Q_2 = 3.15 	imes 10^8 \mathrm{~J} + 1.58 	imes 10^8 \mathrm{~J} = 4.73 	imes 10^8 \mathrm{~J}$$

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