A small quantity mass m, of water at a temperature `theta ("in " ^(@)C)` is poured on to a larger mass M of ice which is at its melting point. If c is the specific heat capacity of water and L the specific heat capacity of water and L the specific latent heat of fusion of ice, then the mass of ice melted is give by

Options

A. `(ML)/(mc theta)`
B. `(Mc theta)/(L)`
C. `(mc theta)/(ML)`
D. `(mc theta)/(L)`

Explanation

To solve the problem of finding the mass of ice melted when a small quantity of water at temperature θ is poured onto a larger mass of ice at its melting point, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the System**: We have a small mass \( m \) of water at temperature \( \theta \) (in °C) and a larger mass \( M \) of ice at 0°C (its melting point).

2. **Apply the Principle of Conservation of Energy**: The heat lost by the water will be equal to the heat gained by the ice. This is based on the principle of conservation of energy.

\[ \text{Heat lost by water} = \text{Heat gained by ice} \]

3. **Calculate Heat Lost by Water**: The heat lost by the water as it cools down to 0°C can be calculated using the formula:

\[ Q_{\text{water}} = mc\theta \]

where \( c \) is the specific heat capacity of water.

4. **Calculate Heat Gained by Ice**: The heat gained by the ice to melt can be expressed as:

\[ Q_{\text{ice}} = m'L \]

where \( m' \) is the mass of ice melted and \( L \) is the specific latent heat of fusion of ice.

5. **Set the Heat Lost Equal to Heat Gained**: According to the conservation of energy:

\[ mc\theta = m'L \]

6. **Solve for the Mass of Ice Melted \( m' \)**: Rearranging the equation to find \( m' \):

\[ m' = \frac{mc\theta}{L} \]

### Final Answer:
The mass of ice melted \( m' \) is given by:

\[ m' = \frac{mc\theta}{L} \]