The mass, specific heat capacity and the temperature of a solid are `1000g,(1)/(2) (cal)/g ^(@)C` and `80^(@)C` respectively. The mass of the liquid and the calorimeter are `900g` and `200g`. Initially,both are at room temperature `20^(@)C` Both calorimeter and the solid are made of same material. In the steady state, temperature of mixture is `40^(@)C`, then specific heat capacity of the unknown liquid.

Explanation

To solve the problem, we need to apply the principle of conservation of energy, which states that the heat lost by the solid will be equal to the heat gained by the liquid and the calorimeter.

### Step-by-Step Solution:

1. **Identify the given values:**
- Mass of solid, \( m_s = 1000 \, \text{g} \)
- Specific heat capacity of solid, \( S_s = \frac{1}{2} \, \frac{\text{cal}}{\text{g} \cdot ^\circ C} \)
- Initial temperature of solid, \( T_{s_i} = 80 \, ^\circ C \)
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