Question

In a steel factory it is found that to maintain M kg of iron in the molten state at its melting point an input power P watt is required. When the power source is turned off, the sample completely solidifies in time. The latent heat of fusion of iron is
\[\begin{align}
  & A.\,\dfrac{2Pt}{M} \\
 & B.\,\dfrac{Pt}{2M} \\
 & C.\,\dfrac{Pt}{M} \\
 & D.\,\dfrac{PM}{T} \\
\end{align}\]

Answer 1

Hint: The latent heat of fusion or the enthalpy of fusion is the amount of energy that must be supplied to a solid substance in order to change its state from the solid state to the liquid state. Thus, the relation between the power, time and the mass gives the latent heat of fusion.

Complete step-by-step solution:
From the given information, we have the data as follows.
In a steel factory it is found that to maintain M kg of iron in the molten state at its melting point an input power P watt is required. When the power source is turned off, the sample completely solidifies in time.
The latent heat of fusion or the enthalpy of fusion is the amount of energy that must be supplied to a solid substance in order to change its state from the solid state to the liquid state.
Initially the iron was maintained at molten state by supplying the power of amount P. Thus, this refers to the fact that the iron lost heat at the rate of P watt. Therefore, when the power is switched off, it starts to lose the heat at the rate of P watt.
In time t heat loss, \[Pt\]
At the time t, iron got solidified.
\[\begin{align}
  & Pt=ML \\
 & \therefore L=\dfrac{Pt}{M} \\
\end{align}\]
\[\therefore \] The latent heat of fusion of iron is,\[\dfrac{Pt}{M}\], thus, option (C) is correct.

Note: Enthalpy of fusion is the other name of the latent heat of fusion. The latent heat of fusion or the enthalpy of fusion is the amount of energy that must be supplied to a solid substance in order to change its state from the solid state to the liquid state.