Which of the following statements does not describe Charles' law ?

Options

A. The volume of a given amount of a gas at constant pressure varies directly as its absolute temperature .
B. For each degree change in temperature , the volume of a sample of a gas changes by the fraction `(1)/(273)` of its volume at `0 .^(@)C`.
C. All gases expand or contract by the same fraction of their volume at `0 .^(@)C` per degree change in temperature .
D. `V_(t) = V_(0) ((273 - t)/(273))`

Explanation

To determine which statement does not describe Charles' Law, let's first summarize what Charles' Law states:

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

2. **Volume Change per Degree**: For each degree change in temperature, the volume of a gas changes by a fraction of \( \frac{1}{273} \) of its volume at 0 degrees Celsius.

3. **Expansion/Contraction**: All gases expand or contract by the same fraction of their volume at 0 degrees Celsius for each degree change in temperature.

Now, let's analyze the provided statements one by one:

### Statement Analysis:

1. **Statement 1**: "The volume of a given amount of a gas at constant pressure varies directly as its absolute temperature."
- **Analysis**: This statement correctly describes Charles' Law. **(Correct)**

2. **Statement 2**: "For each degree change in temperature, the volume of a sample of a gas changes by a fraction of \( \frac{1}{273} \) of its volume at 0 degrees Celsius."
- **Analysis**: This statement is also correct according to Charles' Law. **(Correct)**

3. **Statement 3**: "All gases expand or contract by the same fraction of their volume at 0 degrees Celsius per degree change in the temperature."
- **Analysis**: This statement is correct as per Charles' Law. **(Correct)**

4. **Statement 4**: "There is a formula given: \( V_T = V_0 \frac{273 - T}{273} \)."
- **Analysis**: This formula is incorrect. According to Charles' Law, the correct relationship should be \( V_T = V_0 \left(1 + \frac{T}{273}\right) \) or \( V_T = V_0 \frac{273 + T}{273} \). Therefore, this statement does not describe Charles' Law. **(Incorrect)**

### Conclusion:
The statement that does not describe Charles' Law is **Statement 4**.

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