M g of ice at `0^@C` is to be converted to water at `0^@C`. If L is the latent heat of fusion of ice, the quantity of heat required for the above operation would be

Options

A. ML cal
B. `M/L`
C. `L/M` cal
D. none of these

Answer

To solve the problem of converting M grams of ice at 0°C to water at 0°C, we need to calculate the quantity of heat required for this phase change. The heat required for this process can be determined using the concept of latent heat of fusion.

### Step-by-Step Solution:

1. **Understand the Process**: We are converting ice (solid) at 0°C to water (liquid) at 0°C. This process involves a phase change, which requires energy.

2. **Identify the Latent Heat of Fusion**: The latent heat of fusion (L) is the amount of heat required to convert 1 gram of solid into liquid at its melting point without a change in temperature. For ice, this is a known value.

3. **Use the Formula for Heat Required**: The quantity of heat (Q) required for the phase change can be calculated using the formula:
\[ Q = m \times L \]
where:
- \( Q \) is the heat required,
- \( m \) is the mass of the ice (in grams),
- \( L \) is the latent heat of fusion of ice (in calories per gram).

4. **Substituting Values**: In this case, we have:
- \( m = M \) (the mass of ice),
- \( L \) is given as the latent heat of fusion.

Therefore, the heat required to convert M grams of ice at 0°C to water at 0°C is:
\[ Q = M \times L \]

5. **Final Expression**: The final expression for the quantity of heat required is:
\[ Q = ML \text{ calories} \]

### Conclusion:
The quantity of heat required to convert M grams of ice at 0°C to water at 0°C is \( ML \) calories.

---