How much heat in joules must be added to 1.059 kg of beryllium to change it from a solid at 662°C to a liquid at 1285°C (its melting
point)?
For beryllium: L = 1.35×10 J/kg, L = 3.24×10 J/kg, c = 1820 J/kg C°
To find the amount of heat required to change beryllium from a solid to a liquid, we need to calculate the heat absorbed during the temperature change and the heat absorbed during the phase change.
First, let's calculate the heat absorbed during the temperature change using the formula:
Q = mcΔT
Where:
Q = heat energy absorbed
m = mass of the substance (1.059 kg)
c = specific heat capacity of beryllium (1820 J/kg C°)
ΔT = change in temperature (Tfinal - Tinitial)
ΔT = 1285°C - 662°C = 623°C
Q = (1.059 kg) * (1820 J/kg C°) * (623°C)
Q = 1,077,679.82 J
Next, we need to calculate the heat absorbed during the phase change from solid to liquid using the formula:
Q = mL
Where:
Q = heat energy absorbed
m = mass of the substance (1.059 kg)
L = latent heat of fusion (1.35×10^5 J/kg)
Q = (1.059 kg) * (1.35×10^5 J/kg)
Q = 143,415 J
Finally, we add the two values together to get the total heat required:
Total heat = Q1 + Q2
Total heat = 1,077,679.82 J + 143,415 J
Total heat = 1,221,094.82 J
Therefore, the heat required to change 1.059 kg of beryllium from a solid at 662°C to a liquid at 1285°C is 1,221,094.82 J.