200 g of hot water at `80^(@)C` is added to 300 g of cold water at `10^(@)C`. Calculate the final temperature of the mixture of water. Consider the heat taken by the container to be negligible. [specific heat capacity of water is 4200 `Jkg^(-1)""^(@)C^(-1)`]

Explanation

To calculate the final temperature of the mixture of hot and cold water, we can use the principle of conservation of energy, which states that the heat lost by the hot water will be equal to the heat gained by the cold water.

### Step-by-Step Solution:

1. **Identify the Given Values:**
- Mass of hot water, \( m_H = 200 \, \text{g} = 0.2 \, \text{kg} \)
- Initial temperature of hot water, \( T_H = 80^\circ C \)
- Mass of cold water, \( m_C = 300 \, \text{g} = 0.3 \, \text{kg} \)
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