In the exp of finding sp heat capacity of an unknown sphere `(S_(2))` mass of the sphere and caloreter aro `1000m` and `200gm` respectively and sp heat capacity of calorimeter is equal to `(1)/(2)cal//gm^(@)C` The mass of liquid 9water) used is `900gm` Initially both the water and the calorimeter were at room temp `20.0^(@)C` while used is `900gm` Initially both the water and the calorimeter were at room temp `20.0^(@)C` while the sphere was at temp `800^(@)C` initially If the steady state temp was found to be `40.0^(@)C` estimate sp heat capacity of the unknown sphere `(S_(2))` `(use S_(water) = 1 cal//g^(@)C)` Also fin the maximum permissible error in sp heat capacity of unknown sphere `(S_(2))` mass end specific heats of sphere and calorimater are correctly known) .

Explanation

To find the specific heat capacity of the unknown sphere \( S_2 \), we will use the principle of conservation of energy, which states that the heat lost by the sphere will be equal to the heat gained by the water and the calorimeter.

### Step-by-Step Solution:

1. **Identify Given Values**:
- Mass of the sphere, \( m_{sphere} = 1000 \, \text{g} \)
- Mass of the calorimeter, \( m_{calorimeter} = 200 \, \text{g} \)
- Specific heat capacity of the calorimeter, \( S_{calorimeter} = \frac{1}{2} \, \text{cal/g}^\circ C \)
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