In an experiment on the specific heat of a metal a 0.20 kg block of the metal at `150^(@)`C is dropped in a copper calorimeter (of water equivalent 0.025 kg) containing 150 cc of water at `27^(@)`C. The final temperature is `40^(@)`C. Calcualte the specific heat of the metal. If heat losses to the surroundings are not negligible, is our answer greater or smaller than the actual value of specific heat of the metal?

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 will be equal to the heat gained by the water and the calorimeter.

### Step-by-Step Solution:

1. **Identify Given Data:**
- Mass of the metal block, \( m = 0.20 \, \text{kg} = 200 \, \text{g} \)
- Initial temperature of the metal, \( T_{i, \text{metal}} = 150^\circ C \)
- Final temperature, \( T_f = 40^\circ C \)
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