The melting point of aluminum is 660°C, the latent heat of fusion is 4.00 × 10⁵ J/kg, and its specific heat is 900 J/(kg K). How much heat must be added to 500 g of aluminum at 27°C to completely melt it? A) 485 kJ B) 395 kJ C) 273 kJ D) 147 kJ E) 14 kJ

Question

Quizplus · Accepted Answer

The heat required to melt the aluminum is given by:$$Q = mL$$where m is the mass of the aluminum and L is the latent heat of fusion.$$Q = (0.5 kg)(4.00 × 10^5 J/kg) = 2.00 × 10^5 J$$The heat required to raise the temperature of the aluminum from 27°C to 660°C is given by:$$Q = mcΔT$$where c is the specific heat of the aluminum and ΔT is the change in temperature.$$Q = (0.5 kg)(900 J/(kg K))(660°C - 27°C) = 283.5 kJ$$The total heat required to completely melt the aluminum is:$$Q = 2.00 × 10^5 J + 283.5 kJ = 485 kJ$$

The Melting Point of Aluminum Is 660°C, the Latent Heat