How many grams of ice at ` -14 .^(@)C` are needed to cool 200 gram of water form `25 .^(@)C` to `10 .^(@)C`? Take specific heat of ice `=0.5 cal g^(-1) .^(@)C^(-1)` and latant heat of ice = `80 cal g^(-1)` .

Explanation

To solve the problem of how many grams of ice at -14°C are needed to cool 200 grams of water from 25°C to 10°C, we will apply the principle of conservation of energy, where the heat lost by the water will be equal to the heat gained by the ice.

### Step-by-Step Solution:

1. **Calculate the Heat Lost by Water (Q1)**:
The heat lost by the water can be calculated using the formula:
\[
Q_1 = m_w \cdot c_w \cdot \Delta T_w
...