To determine how much heat is needed to melt 15.0 kg of lead at its melting point, we will use the given latent heat of fusion for lead and apply the formula for calculating the heat required for a phase change.
The formula to calculate the heat required to melt a given mass of a substance is:
[tex]\[ Q = m \cdot L_f \][/tex]
where:
- [tex]\( Q \)[/tex] = heat required (in joules, J)
- [tex]\( m \)[/tex] = mass of the substance (in kilograms, kg)
- [tex]\( L_f \)[/tex] = latent heat of fusion of the substance (in joules per kilogram, J/kg)
From the given data:
- The latent heat of fusion ([tex]\( L_f \)[/tex]) for lead is [tex]\( 0.25 \times 10^5 \, \text{J/kg} \)[/tex] (or 25000 J/kg).
- The mass ([tex]\( m \)[/tex]) of lead that needs to be melted is 15.0 kg.
Using the formula:
[tex]\[ Q = m \cdot L_f \][/tex]
[tex]\[ Q = 15.0 \, \text{kg} \cdot 25000 \, \text{J/kg} \][/tex]
[tex]\[ Q = 375000 \, \text{J} \][/tex]
Thus, the heat required to melt 15.0 kg of lead at its melting point is 375000 J, which corresponds to the option:
[tex]\[ \boxed{3.75 \times 10^5 \, \text{J}} \][/tex]
So, the correct answer is 3.75 E5 J.
