Question

How much energy is required to melt $ 1.5kg $ of lead?

Answer 1

Hint : Let us first understand what is meant by melting point and specific heat. The temperature at which the substance converts from solid state to liquid state is known as melting point. The amount of heat required to rise the temperature of a substance by one degree Celsius per unit mass of a substance.

Complete Step By Step Answer:
According to the principle of calorimetric, the total heat lost by the hot body is equal to the total heat gained by the cold body. This principle indicates the law of conservation of energy. Here we have; the enthalpy of fusion (energy needed to change state from solid to liquid) of lead is $ 4.77\text{ }kJ/mol $ (so it takes $ 4.77\text{ }kJ $ to melt one mole of lead). We need to find the number of moles (n) of lead in $ 1.5kg $ (m).
The formula here is $ n=\dfrac{m}{M} $ , from the periodic table, M=207.2g/mol.
Therefore, substituting all the values in the equation so that we acquire the values of number of moles;
 $ n=\dfrac{m}{M}=\dfrac{1500g}{207.2g\cdot mo{{l}^{-1}}}=7.24moles $
Thus, the number of moles is $ 7.24 $ moles.
Now, we know that Energy $ Energy=\left( 7.24moles \right)\times \left( 4.77kJ\cdot mo{{l}^{-1}} \right) $
 $ \Rightarrow $ Correct answer is Energy equal to $ 34.53kJ. $
Therefore, $ 34.53kJ $ energy is required to melt $ 1.5kg $ of lead.

Note :
Do not get confused between latent heat and specific heat. Latent heat is the energy required by a substance to undergo a phase change. Specific heat is the amount of heat required by one gram of a substance to rise the temperature by one degree Celsius. Remember that specific is not applicable when a substance undergoes a phase change.