A metal piece of mass 20 g is heated to a constant temperature of `100^@`C. Then it is added in a calorimeter of mass 50 g and specific heat capacity 0.42 J `g^(-1) K^(-1)`, containing 50 g of water at `20^@`C. After stirring the water, the highest temperature recorded is `22^@`C. Calculate the specific heat capacity of metal.
Specific heat capacity of water = `4.2 J g^(-1)K^(-1)`

Explanation

To solve the problem of finding the specific heat capacity of the metal piece, we will use the principle of conservation of energy. The heat lost by the metal will be equal to the heat gained by the water and the calorimeter.

### Step-by-Step Solution:

1. **Identify the given values:**
- Mass of the metal piece, \( m_m = 20 \, \text{g} \)
- Initial temperature of the metal, \( T_{m_i} = 100 \, ^\circ C \)
- Mass of the calorimeter, \( m_c = 50 \, \text{g} \)
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