Which of the following equations does not represent Charles' law for a given mass of gas at constant pressure?

Options

A. `(V)/(T)=K`
B. log V = log K+ log T
C. log K = log V + log T
D. `(d(In V))/(dt)=(1)/(T)`

Explanation

To determine which equation does not represent Charles' law for a given mass of gas at constant pressure, we first need to understand what Charles' law states.

### Step-by-Step Solution:

1. **Understanding Charles' Law**:
Charles' law states that at constant pressure, the volume (V) of a gas is directly proportional to its absolute temperature (T). This can be mathematically expressed as:
\[ V \propto T \quad \text{(at constant pressure)} \]

2. **Mathematical Representation**:
From the proportionality, we can write:
\[ \frac{V}{T} = k \]
where \( k \) is a constant.

3. **Analyzing Each Option**:
- **Option A**: \( \frac{V}{T} = k \) - This is a correct representation of Charles' law.
- **Option B**: Taking the logarithm gives \( \log V - \log T = \log k \), which rearranges to \( \log V = \log k + \log T \). This is also correct.
- **Option C**: We need to check this option closely. If it does not match the form of Charles' law, it is the incorrect one.
- **Option D**: If we differentiate the logarithmic form, we can show that it aligns with the principles of Charles' law.

4. **Identifying the Incorrect Option**:
After analyzing all options:
- Options A, B, and D align with Charles' law.
- Option C does not match the expected form of Charles' law.

5. **Conclusion**:
Therefore, the equation that does not represent Charles' law is:
\[ \text{Option C} \]