A substance of mass M kg requires a power input of P wants to remain in the molten state at its melting point. When the power source is turned off, the sample completely solidifies in time t seconds. The latent heat of fusion of the substance is …….

Options

A. `2 Pt//M`
B. `Pt//2M`
C. `Pt//M`
D. `PM//t`

Answer

To solve the problem, we will use the concepts of heat transfer and the latent heat of fusion. Here’s a step-by-step solution:

### Step 1: Understand the Problem
The substance of mass \( M \) kg requires a power input of \( P \) watts to remain in the molten state. When the power is turned off, the substance solidifies completely in time \( t \) seconds. We need to find the latent heat of fusion \( L \) of the substance.

### Step 2: Calculate the Heat Released
When the power source is turned off, the heat released by the substance as it solidifies can be calculated using the formula:
\[ \text{Heat released} = P \times t \]
where \( P \) is the power in watts and \( t \) is the time in seconds.

### Step 3: Relate Heat Released to Latent Heat
During the phase change from liquid to solid, the heat released is also equal to the product of the mass of the substance and its latent heat of fusion \( L \):
\[ \text{Heat released} = M \times L \]

### Step 4: Set the Two Heat Equations Equal
Since the heat released during solidification is equal to the heat absorbed during the phase change, we can set the two equations from Steps 2 and 3 equal to each other:
\[ P \times t = M \times L \]

### Step 5: Solve for Latent Heat of Fusion \( L \)
To find the latent heat of fusion \( L \), we rearrange the equation:
\[ L = \frac{P \times t}{M} \]

### Final Answer
The latent heat of fusion of the substance is:
\[ L = \frac{P \times t}{M} \]

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