When 400 J of heat are added to a 0.1 kg sample of metal, its temperature increase by `20(@)`C. What isthe specific heat of the metal?

Options

A. 200J/Kg C
B. 300 J/Kg c
C. 400J/Kg c
D. 100J/Kg c

Explanation

To find the specific heat of the metal, we can use the formula for heat transfer:

\[ Q = m \cdot s \cdot \Delta T \]

Where:
- \( Q \) is the heat added (in joules),
- \( m \) is the mass of the substance (in kg),
- \( s \) is the specific heat capacity (in J/kg°C),
- \( \Delta T \) is the change in temperature (in °C).

### Step-by-Step Solution:

1. **Identify the given values**:
- Heat added, \( Q = 400 \, \text{J} \)
- Mass of the metal, \( m = 0.1 \, \text{kg} \)
- Change in temperature, \( \Delta T = 20 \, \text{°C} \)

2. **Substitute the values into the formula**:
\[ 400 = 0.1 \cdot s \cdot 20 \]

3. **Simplify the equation**:
- First, calculate \( 0.1 \cdot 20 \):
\[ 0.1 \cdot 20 = 2 \]
- Now the equation becomes:
\[ 400 = 2s \]

4. **Solve for \( s \)**:
- Divide both sides by 2:
\[ s = \frac{400}{2} = 200 \, \text{J/kg°C} \]

5. **Conclusion**:
- The specific heat of the metal is \( 200 \, \text{J/kg°C} \).

### Final Answer:
The specific heat of the metal is \( 200 \, \text{J/kg°C} \).

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