Which of the following curves represent(s) Boyle's law?

Options

A.
B.
C.
D.

Explanation

To determine which curves represent Boyle's law, we need to understand the relationship between pressure (P) and volume (V) of a gas at constant temperature. Boyle's law states that the pressure of a given mass of gas is inversely proportional to its volume when the temperature is held constant. This can be mathematically expressed as:

\[ P \propto \frac{1}{V} \]

or

\[ PV = k \]

where \( k \) is a constant.

### Step-by-Step Solution:

1. **Understanding Boyle's Law**:
- Boyle's law states that at constant temperature, the product of pressure and volume for a fixed amount of gas is constant. This means that if the volume increases, the pressure decreases, and vice versa.

2. **Graphical Representation**:
- The relationship between pressure and volume can be graphically represented. Since pressure is inversely proportional to volume, the graph of P vs. V will be a rectangular hyperbola. This means that as you plot pressure (P) on the y-axis and volume (V) on the x-axis, the curve will approach both axes but never touch them.

3. **Identifying the Curves**:
- **Curve A**: If this curve is a rectangular hyperbola, then it represents Boyle's law.
- **Curve B**: If this curve represents the relationship of \( \frac{1}{P} \) versus V, it will be a straight line through the origin, indicating that \( \frac{1}{P} \) is directly proportional to V. This is also consistent with Boyle's law.
- **Curve C**: If this curve represents a constant product \( PV = k \), it will also reflect Boyle's law.
- **Curve D**: If this curve represents pressure versus \( \frac{1}{V} \), it will again be a straight line indicating that pressure is directly proportional to \( \frac{1}{V} \), which is consistent with Boyle's law.

4. **Conclusion**:
- All the curves (A, B, C, and D) represent Boyle's law in different forms. Thus, the answer is that all options are correct.