According to Boyle's law, PV = constant, at constant temperature. Which of the following graphs is correct?

Options

A.
B.
C.
D.

Answer

To solve the question regarding Boyle's law and identify the correct graph, we can follow these steps:

### Step-by-Step Solution:

1. **Understand Boyle's Law**: Boyle's law states that for a given mass of gas at constant temperature, the product of pressure (P) and volume (V) is constant. Mathematically, this can be expressed as:
\[ PV = k \]
where \( k \) is a constant.

2. **Identify the Relationship**: Since \( PV \) is constant, if we increase the pressure (P), the volume (V) must decrease to keep the product \( PV \) constant, and vice versa.

3. **Analyze the Graphs**: We need to evaluate the provided graphs to see which one correctly represents the relationship described by Boyle's law.

- **Graph 1**: If \( PV \) is on the Y-axis and pressure (P) is on the X-axis, as pressure increases, \( PV \) should remain constant. This graph would show an increasing trend, which is incorrect.

- **Graph 2**: If \( PV \) is on both axes, as pressure increases, \( PV \) should not change. This graph would show a changing trend, which is also incorrect.

- **Graph 3**: If \( PV \) is on the Y-axis and pressure (P) is on the X-axis, and the graph shows a decreasing trend as pressure increases, this indicates that \( PV \) is not constant, which is again incorrect.

- **Graph 4**: This graph shows a horizontal line, indicating that \( PV \) remains constant regardless of changes in pressure. This is the correct representation of Boyle's law.

4. **Conclusion**: Based on the analysis of the graphs, the correct graph that represents Boyle's law is the one that shows \( PV \) as a constant value, which is option number 4.

### Final Answer:
The correct graph according to Boyle's law is **Option 4**.

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