A calorimeter of mass 50 g and specific heat capacity `0.42Jg^(-1)""^(@)C^(-1)` contains some mass of water at 20°C. A metal piece of mass 20 g at `100^(@)C` is dropped into the calorimeter. After stirring, the final temperature of the mixture is found to be `22^(@)C`. Find the mass of water used in the calorimeter.
[specific heat capacity of the metal piece = `0.3Jg^(-1)""^(@)C^(-1)`
specific heat capacity of water = `4.2Jg^(-1)""^(@)C^(-1)`]

Explanation

To solve the problem step by step, we will use the principle of conservation of energy, which states that the heat lost by the metal piece will be equal to the heat gained by the calorimeter and the water in it.

### Step 1: Identify the given values
- Mass of the metal piece (m1) = 20 g
- Specific heat capacity of the metal piece (c1) = 0.3 J/g°C
- Initial temperature of the metal piece (T_initial_metal) = 100°C
- Final temperature of the mixture (T_final) = 22°C
- Mass of the calorimeter (m_calorimeter) = 50 g
...