A sphere of alumininum of mass 0.047 kg placed for sufficient time in a vessel containing boling 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^(@)C` . calculate the specific heat capacity of aluminum. Specific heat capacity of copper = `0.386 xx 10^(3) J kg^(-1) K^(-1)`.
Specific heat capacity of water = `4.18 xx 10^(-3) J kg^(-1) K^(-1)`

Explanation

To solve the problem, 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 copper calorimeter and the water.

### Step-by-Step Solution:

1. **Identify the known values:**
- Mass of aluminum sphere, \( m_{Al} = 0.047 \, \text{kg} \)
- Initial temperature of aluminum, \( T_{Al} = 100^\circ C \)
- Mass of copper calorimeter, \( m_{Cu} = 0.14 \, \text{kg} \)
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