The S.I. unit of specific heat capacity is

Options

A. `JK^(-1)`
B. `J kg ^(-1)`
C. `" J mol "^(-1) K^(-1)`
D. `J kg ^(-1) K^(-1)`

Answer

To find the S.I. unit of specific heat capacity, we can follow these steps:

### Step 1: Understand the Definition
Specific heat capacity (s) is defined as the amount of heat (Q) required to raise the temperature of 1 kg of a substance by 1 degree Celsius (or 1 Kelvin).

### Step 2: Write the Formula
The relationship can be expressed mathematically as:
\[ Q = m \cdot s \cdot \Delta T \]
Where:
- \( Q \) = heat added (in Joules)
- \( m \) = mass of the substance (in kg)
- \( s \) = specific heat capacity (in J/kg·K)
- \( \Delta T \) = change in temperature (in degrees Celsius or Kelvin)

### Step 3: Rearrange the Formula
To find the specific heat capacity, we can rearrange the formula:
\[ s = \frac{Q}{m \cdot \Delta T} \]

### Step 4: Determine the Units
Now, we need to determine the units of each component in the formula:
- The unit of heat (Q) is Joules (J).
- The unit of mass (m) is kilograms (kg).
- The unit of temperature change (ΔT) is Kelvin (K).

### Step 5: Substitute the Units
Substituting the units into the rearranged formula gives:
\[ s = \frac{\text{J}}{\text{kg} \cdot \text{K}} \]

### Step 6: Write the Final Answer
Thus, the S.I. unit of specific heat capacity is:
\[ \text{J kg}^{-1} \text{K}^{-1} \]

### Conclusion
The correct answer is:
**Joule per kilogram per Kelvin (J kg⁻¹ K⁻¹)**.