Answer :

The heat is needed to completely melt 20kg of lead that was initially at 27°C is approximately 498.5 megajoules (MJ)

We need to calculate the heat required using the specific heat capacity and the latent heat of fusion for lead. The specific heat capacity of lead is 0.13 J/g°C, and the latent heat of fusion is 24.5 kJ/kg. First, we need to convert the mass of lead from kg to grams: 20kg x 1000g/kg = 20,000g.

To raise the temperature of the lead from 27°C to its melting point, we need to calculate the heat using the equation Q = mcΔT

Where:

Q = heat

m=mass

c = specific heat capacity

ΔT = change in temperature.

Q = (20,000g)(0.13 J/g°C)(327°C) = 8,514,000 J.

Next, we need to calculate the heat required for the phase change from solid to liquid. The equation Q = mL is used, where L is the latent heat of fusion.
Q = (20,000g)(24.5 kJ/kg) = 490,000 kJ = 490,000,000 J.
Finally, we add the heat for raising the temperature and the heat for phase change together: 8,514,000 J + 490,000,000 J = 498,514,000 J.
Therefore, approximately 498.5 megajoules (MJ) of heat is needed to completely melt 20kg of lead initially at 27°C.

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