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?

use the following values:
For copper:
c_copper=0.386 kJ/kg.K
T_fusion=1359 K
L_fusion=205 kg/K

To determine how much heat must flow into the aluminum block in order to melt it, we need to consider the energy required for both raising the temperature of the block to its melting point and for the actual phase change from solid to liquid.

Here's how we can calculate it:

1. First, calculate the energy required to raise the temperature of the aluminum block to its melting point. We can use the specific heat capacity formula:

Q = mcΔT

where Q is the heat energy, m is the mass of the block, c is the specific heat capacity of aluminum, and ΔT is the change in temperature.

Given:
Mass of the block (m) = 1.67 kg
Specific heat capacity of aluminum (c_aluminum) = 0.386 kJ/kg.K
Initial temperature (T_initial) = 21.7°C = 21.7 + 273.15 = 294.85 K
Melting point (T_fusion) = 1359 K

ΔT = T_fusion - T_initial
ΔT = 1359 K - 294.85 K
ΔT = 1064.15 K

Q = (1.67 kg) × (0.386 kJ/kg.K) × (1064.15 K)

2. Next, calculate the energy required for the phase change from solid to liquid. This can be calculated using the formula:

Q = mL_fusion

where Q is the heat energy, m is the mass of the block, and L_fusion is the specific latent heat of fusion for aluminum.

Given:
Specific latent heat of fusion for aluminum (L_fusion) = 205 kJ/kg.K

Q = (1.67 kg) × (205 kJ/kg)

3. Finally, add the two values calculated in steps 1 and 2 to get the total heat energy required:

Total Q = Q1 + Q2

where Q1 is the energy required to raise the temperature and Q2 is the energy required for the phase change.

Total Q = Q1 + Q2

Therefore, you can calculate the total heat energy required to melt the aluminum block by substituting the given values into the equations and performing the necessary calculations.