Charle's law may be expressed as

Options

A. `(dV//dT)_(P) = K`
B. `(dV//dT)_(P) = KT`
C. `(dV//dT_(P) = - K//T^(2)`
D. `V = KT`

Explanation

To express Charles's Law, we start with the fundamental relationship it describes. Charles's Law states that at constant pressure, the volume of a gas is directly proportional to its absolute temperature.

### Step-by-Step Solution:

1. **Understanding the Law**:
- Charles's Law applies when the pressure of a gas is held constant.

2. **Establishing the Relationship**:
- The relationship can be mathematically expressed as:
\[ V \propto T \]
- This means that if the temperature (T) increases, the volume (V) also increases, provided the pressure remains constant.

3. **Introducing the Constant of Proportionality**:
- To convert the proportionality into an equation, we introduce a constant (k):
\[ V = kT \]

4. **Differentiating the Equation**:
- If we want to express the change in volume with respect to temperature, we can differentiate the equation:
\[ \frac{dV}{dT} = k \]
- This indicates that the rate of change of volume with respect to temperature is equal to the constant k at constant pressure.

5. **Conclusion**:
- Therefore, Charles's Law can be expressed in two forms:
- \( V = kT \) (Volume is directly proportional to temperature)
- \( \frac{dV}{dT} = k \) (Rate of change of volume with respect to temperature)

### Final Answer:
Charles's Law may be expressed as:
- \( V = kT \) (Option D)
- \( \frac{dV}{dT} = k \) (First option is also correct)