A bucket contains 8 kg of water at `25^@`C. 2 kg of water at `80^@`C is poured into it. Neglecting the heat energy absorbed by the bucket, calculate the final temperature of water.

Explanation

To solve the problem of finding the final temperature of the water after mixing, we can use the principle of conservation of energy. 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 masses and initial temperatures:**
- Mass of cold water, \( m_1 = 8 \, \text{kg} \)
- Initial temperature of cold water, \( T_1 = 25^\circ C \)
- Mass of hot water, \( m_2 = 2 \, \text{kg} \)
...