Which of the following is a unit of specifi heat?

Options

A. `Jkg.^(@)C^(-1)`
B. `kJ//kg.^(@)C`
C. `kg.^(@)C//J`
D. `J//kg.^(@)C^(-2)`

Answer

To determine the unit of specific heat, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Formula for Specific Heat**:
The specific heat (s) is defined by the formula:
\[ Q = m \cdot s \cdot \Delta T \]
where:
- \( Q \) = heat supplied (in Joules)
- \( m \) = mass of the substance (in kg)
- \( s \) = specific heat (in J/kg°C)
- \( \Delta T \) = change in temperature (in °C)

2. **Rearranging the Formula**:
To find the specific heat, we can rearrange the formula:
\[ s = \frac{Q}{m \cdot \Delta T} \]

3. **Identify the Units**:
- The unit of heat \( Q \) is Joules (J).
- The unit of mass \( m \) is kilograms (kg).
- The unit of change in temperature \( \Delta T \) is degrees Celsius (°C).

4. **Substituting the Units**:
Substituting the units into the rearranged formula gives:
\[ s = \frac{\text{J}}{\text{kg} \cdot \text{°C}} \]

5. **Final Unit of Specific Heat**:
Therefore, the unit of specific heat can be expressed as:
\[ \text{J/kg°C} \quad \text{or} \quad \text{kJ/kg°C} \quad \text{(since 1 kJ = 1000 J)} \]

6. **Evaluating the Options**:
From the options provided, we need to identify which one matches the derived unit of specific heat. The correct option is:
- **kJ/kg°C** (kilojoules per kilogram per degree Celsius)

### Conclusion:
The correct unit of specific heat is **kJ/kg°C**.

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