which in not correct curve for Gay-luacc's law ?

Options

A.
B.
C.
D.

Explanation

To determine which curve is not correct for Gay-Lussac's law, we need to understand the relationship defined by this law. Gay-Lussac's law states that the pressure of a fixed amount of gas is directly proportional to its absolute temperature when the volume is held constant.

### Step-by-Step Solution:

1. **Understand Gay-Lussac's Law**:
- Gay-Lussac's law can be expressed mathematically as:
\[ P \propto T \quad \text{(at constant volume)} \]
- This means that if the temperature increases, the pressure also increases, and vice versa.

2. **Identify the Variables**:
- In the equation \(PV = nRT\), for a fixed amount of gas (constant \(n\)) and constant volume (\(V\)), we can simplify it to:
\[ P = kT \]
- Here, \(k\) is a constant that depends on the amount of gas and the volume.

3. **Graphical Representation**:
- If we plot pressure \(P\) on the y-axis and temperature \(T\) on the x-axis, the graph should be a straight line passing through the origin, indicating a direct proportionality.

4. **Analyze the Given Options**:
- Option B (P vs. T) is correct as it represents a straight line.
- Option C (P/T vs. T) should be constant, indicating that as temperature increases, \(P/T\) remains constant. This means the graph should be a horizontal line.
- Option D is where we need to be careful. If \(P/T\) is plotted against \(T\), it should not increase with \(T\) since \(P/T\) is constant.

5. **Conclusion**:
- After analyzing the options, we find that option D is incorrect because it suggests that \(P/T\) increases with temperature, which contradicts Gay-Lussac's law.

### Final Answer:
The incorrect curve for Gay-Lussac's law is **Option D**.

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