A 1.67-kg block of aluminum at 21.7°C is to be melted and reshaped. How much heat must flow into the block in order to melt it?

c_aluminum=0.386 kJ/kg.K
T_fusion=1359 K
L_fusion=205 kg/K

To find the amount of heat required to melt the block of aluminum, we need to first calculate the heat required to raise the temperature of the aluminum from 21.7°C to its melting point, and then the heat required for the phase change from solid to liquid.

1. Calculate the heat required to raise the temperature:
The specific heat capacity of aluminum, denoted as c_aluminum, is given as 0.386 kJ/kg.K. Since we have a 1.67 kg block of aluminum, we can multiply the mass by the specific heat capacity and the change in temperature to calculate the heat required.

Heat_required1 = mass_aluminum * c_aluminum * change_in_temperature

Substituting the known values:
mass_aluminum = 1.67 kg
c_aluminum = 0.386 kJ/kg.K
change_in_temperature = T_fusion - initial_temperature

Where initial_temperature = 21.7°C and T_fusion = 1359 K.

Therefore, the heat required to raise the temperature of the aluminum to its melting point is:

Heat_required1 = 1.67 kg * 0.386 kJ/kg.K * (1359 K - (21.7°C + 273.15 K))

2. Calculate the heat required for phase change:
The heat required for phase change, also known as the latent heat of fusion, is denoted as L_fusion and is given as 205 kJ/kg. To calculate the heat required for phase change, we need to multiply the mass of the aluminum by the latent heat of fusion.

Heat_required2 = mass_aluminum * L_fusion

Substituting the known values:
mass_aluminum = 1.67 kg
L_fusion = 205 kJ/kg

Therefore, the heat required for phase change is:

Heat_required2 = 1.67 kg * 205 kJ/kg

3. Calculate the total heat required:
To find the total heat required, we add the heat required to raise the temperature and the heat required for phase change:

Total_heat_required = Heat_required1 + Heat_required2

Now you can substitute the calculated values to find the total heat required.