A sphere of aluminium of 0.047 kg is placed for sufficient time in a vessel containing boiling water, so that the sphere is at `100^(@)` C. It is then immediately transferred to 0.14 kg copper calorimeter containing 0.25 kg of water at `20^(@)` C. The temperature of water rises and attains a steady state at `23^(@)`Calculate the specific heat capacity of aluminium. (Give specific heat of copper `=0.386xx10^(3)Jkg^(-1)K^(-1))`.

Explanation

To solve the problem of finding the specific heat capacity of aluminum, we will use the principle of conservation of energy, which states that the heat lost by the aluminum sphere will be equal to the heat gained by the water and the copper calorimeter.

### Step-by-Step Solution:

1. **Identify Given Data:**
- Mass of aluminum sphere, \( m_1 = 0.047 \, \text{kg} \)
- Initial temperature of aluminum, \( T_{i1} = 100 \, \text{°C} \)
- Final temperature of the system, \( T_f = 23 \, \text{°C} \)
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