Which of the following relationships for various gas laws is not correct ?

Options

A. `V_(t) = V_(0) + (V_(0))/(273)xx t`
B. `(V_(1))/(T_(1)) = (V_(2))/(T_(2))` (constant P)
C. `(P_(1))/(T_(1)) = (P_(2))/(T_(2))` (constant V)
D. `(P_(1)T_(1))/(V_(1)) = (P_(2)T_(2))/(V_(2))`

Answer

To determine which of the following relationships for various gas laws is not correct, we need to analyze the relationships stated in the question.

### Step-by-Step Solution:

1. **Understand the Gas Laws**:
- **Boyle's Law**: At constant temperature (T), the pressure (P) of a gas is inversely proportional to its volume (V). Mathematically, this is expressed as \( P \propto \frac{1}{V} \) or \( PV = k \) (where k is a constant).
- **Charles's Law**: At constant pressure (P), the volume (V) of a gas is directly proportional to its temperature (T). This can be expressed as \( V \propto T \) or \( \frac{V}{T} = k \).
- **Gay-Lussac's Law**: At constant volume (V), the pressure (P) of a gas is directly proportional to its temperature (T). This is expressed as \( P \propto T \) or \( \frac{P}{T} = k \).

2. **Analyze Each Statement**:
- **Statement A**: This is correct if it states a valid relationship according to the gas laws.
- **Statement B**: If it states that at constant T, V is directly proportional to T, this is incorrect as it should be \( V \propto T \) at constant P.
- **Statement C**: If it states that T is directly proportional to T at constant V, this is trivially true but not informative.
- **Statement D**: If it states that P is directly proportional to T1 and P is directly proportional to T and inversely proportional to V1, this is a contradiction and thus incorrect.

3. **Identify the Incorrect Relationship**:
- After analyzing the relationships, it appears that the relationship in Statement D does not hold true as it contradicts the basic principles of gas laws.

### Conclusion:
The answer to the question is that the relationship stated in **Statement D** is not correct.

---