How much heat in joules must be added to 0.348 kg of aluminum to change it from a solid at 138 °C to a liquid at 660 °C (its melting point)? The latent heat of fusion for aluminum is 4.0 x 105 J/kg.
To solve this problem, we need to calculate the heat required in two steps:
Step 1: Calculate the heat required to raise the temperature of aluminum from the initial temperature to its melting point.
Step 2: Calculate the heat required for the phase change from solid to liquid.
Step 1: Calculate the heat required to raise the temperature of aluminum:
The specific heat capacity of aluminum is 900 J/kg·°C.
The formula to calculate the heat required to change the temperature is:
Q = mcΔT
Where:
Q = heat (in Joules)
m = mass of the substance (in kilograms)
c = specific heat capacity (in Joules per kilogram per degree Celsius)
ΔT = change in temperature (in degrees Celsius)
In this case:
m = 0.348 kg (mass of aluminum)
c = 900 J/kg·°C (specific heat capacity of aluminum)
ΔT = (660 °C - 138 °C) = 522 °C (change in temperature)
Q1 = 0.348 kg * 900 J/kg·°C * 522 °C
Step 2: Calculate the heat required for phase change:
The latent heat of fusion for aluminum is 4.0 x 10^5 J/kg.
The formula to calculate the heat required for the phase change is:
Q = mL
Where:
Q = heat (in Joules)
m = mass of the substance (in kilograms)
L = latent heat of fusion (in Joules per kilogram)
In this case:
m = 0.348 kg (mass of aluminum)
L = 4.0 x 10^5 J/kg (latent heat of fusion of aluminum)
Q2 = 0.348 kg * 4.0 x 10^5 J/kg
Finally, we can calculate the total heat required:
Total heat (Q_total) = Q1 + Q2
Q_total = Q1 + Q2
You can substitute the values into the formulas and calculate the total heat in joules needed to change the aluminum from solid at 138 °C to a liquid at 660 °C.
Look up the specific heat of aluminum. Call it C.
Q = M C *(522) + M*(4.0*10^5)
Where M= 0.348 kg
Compute the heat required, Qj