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How much heat energy (in megajoules) must be applied to melt 50 kg of lead at 20°C? (Hint: The melting point of lead is 327°C, and the specific heat of lead is 0.031.)

User Jhurtado
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1 Answer

3 votes
We can solve the problem splitting in two steps.

1) First, we need to raise the temperature of the block of lead from
20^(\circ)C to its melting temperature (
327 ^(\circ)). The quantity of heat needed for this process is

Q_1 = m C_s \Delta T
where
m=50 kg is the mass,
C_s = 0.031 kcal /(kg K) = 0.13 kJ/(kg K) is the specific heat of lead, and
\Delta T=(327-20)^(\circ)C=307 ^(\circ)C=307 K is the variation of temperature.
Calculating:

Q_1 = (50 kg)(0.13 kJ/(kgK))(307 K)=1995 kJ=2.00 MJ

2) Once the block of lead has reached its melting temperature, we must add other heat to cause the complete fusion of the block. The amount of heat need in this process is

Q_2 = m L
where
L=22.4 kJ/kg is the latent heat of fusion of lead. Therefore we have

Q_2 = (50 kg)(22.4 kJ/kg)=1120 kJ=1.12 MJ

3) And so, the total amount of heat needed for the entire process is

Q=Q_1+Q_2 = 2.00MJ+1.12 MJ=3.12 MJ
User Fabrice Leyne
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