Which of the following plots are correct for an ideal gas ?

Options

A.
B.
C.
D.

Answer

To determine which plots are correct for an ideal gas, we will analyze each graph based on the fundamental gas laws: Boyle's Law, Charles's Law, and Gay-Lussac's Law.

### Step-by-Step Solution:

1. **Understanding Boyle's Law**:
- Boyle's Law states that at constant temperature, the pressure (P) of a gas is inversely proportional to its volume (V).
- Mathematically, this can be expressed as: \( P \propto \frac{1}{V} \) or \( PV = k \) (where k is a constant).

2. **Analyzing the First Graph (P vs. 1/V)**:
- The first graph plots pressure (P) against the reciprocal of volume (1/V).
- According to Boyle's Law, if \( P \propto \frac{1}{V} \), then this relationship will yield a straight line when plotted as P vs. 1/V.
- **Conclusion**: This graph is correct.

3. **Analyzing the Second Graph (PV vs. P)**:
- The second graph plots the product of pressure and volume (PV) against pressure (P) at constant temperature.
- According to Boyle's Law, \( PV = k \) is a constant, which means that if we plot PV against P, it should yield a horizontal line (constant value) parallel to the pressure axis.
- **Conclusion**: This graph is incorrect as it does not represent a constant value.

4. **Analyzing the Third Graph (V vs. T)**:
- The third graph plots volume (V) against temperature (T) at constant pressure.
- According to Charles's Law, volume is directly proportional to temperature: \( V \propto T \).
- This relationship yields a straight line with a constant slope when plotted.
- **Conclusion**: This graph is correct.

5. **Analyzing the Fourth Graph (P vs. T)**:
- The fourth graph plots pressure (P) against temperature (T) at constant volume.
- According to Gay-Lussac's Law, pressure is directly proportional to temperature: \( P \propto T \).
- This relationship also yields a straight line with a constant slope when plotted.
- However, if the graph shown is parallel to the temperature axis, it suggests that pressure does not change with temperature, which is incorrect.
- **Conclusion**: This graph is incorrect.

### Final Answer:
The correct plots for an ideal gas are **Option A (P vs. 1/V)** and **Option C (V vs. T)**.