A 100 g cube of aluminium is removed from a bath of boiling water and dropped in a bath of room temperature water (2.00 litres at `20.0^(@)C`). What is the final temperature of the water assuming heat loss to the surroundings is negligible? The specific heat capacity of aluminium is 897 J/kg`.^(@)C`.

Explanation

To solve the problem step by step, we will apply the principle of conservation of energy, which states that the heat lost by the aluminum cube will be equal to the heat gained by the water.

### Step 1: Identify the given data
- Mass of aluminum cube, \( m_{Al} = 100 \, \text{g} = 0.1 \, \text{kg} \)
- Initial temperature of aluminum, \( T_{Al_i} = 100 \, ^\circ C \)
- Volume of water, \( V_{water} = 2 \, \text{liters} = 2 \times 10^{-3} \, \text{m}^3 \)
- Initial temperature of water, \( T_{water_i} = 20 \, ^\circ C \)
- Specific heat capacity of aluminum, \( c_{Al} = 897 \, \text{J/kg} \cdot ^\circ C \)
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