Lead melt

Find the heat needed to melt an object made of lead weighing 250g and an initial temperature of 35°C. Lead melts at 327°C at normal pressure. Mass heat capacity of lead c = 129 J/kg • K and mass latent heat of lead lt (t is the subscript) = 22.6 kJ/kg.

Correct answer:

Q =  15.067 kJ

Step-by-step explanation:

$$\begin{gathered} m=250\text{g}\to \text{kg}=250:1000\text{kg}=0.25\text{kg} \\ {t}_1=35\text{°C} \\ {t}_2=327\text{°C} \\ c=129\text{J/kg/K} \\ l=22.6\text{kJ/kg} \\ T=t_2-t_1=327-35=292\text{K} \\ {Q}_1=m\cdot c\cdot T=0.25\cdot 129\cdot 292=9417\text{J} \\ {Q}_2=l\cdot m=22.6\cdot 0.25=\frac{113}{20}=5.65\text{kJ} \\ Q=Q_1/1000+Q_2=9417/1000+5.65=15.067\text{kJ} \end{gathered}$$

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