When 0.15 kg of ice at `0^(@)C` is mixed with 0.30 kg of water at `50^(@)C` in a container, the resulting temperature is `6.7^(@)C`. Calculate the heat of fusion of ice. `(s_(water) = 4186 J kg^(-1)K^(-1))`

Explanation

To calculate the heat of fusion of ice when 0.15 kg of ice at 0°C is mixed with 0.30 kg of water at 50°C, resulting in a final temperature of 6.7°C, we can follow these steps:

### Step 1: Identify the heat loss from water
The heat lost by the water as it cools down from 50°C to 6.7°C can be calculated using the formula:
\[ Q_{\text{loss}} = M_w \cdot s_w \cdot \Delta T \]
where:
- \( M_w = 0.30 \, \text{kg} \) (mass of water)
- \( s_w = 4186 \, \text{J/kg/K} \) (specific heat of water)
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