Which one of these graphs for an ideal gas havinga fixed amount, the arrow indication, is incorrectly marked ?

Options

A.
B.
C.
D.

Explanation

To determine which graph for an ideal gas with a fixed amount is incorrectly marked, we will analyze the relationships between pressure (P), volume (V), and temperature (T) based on the ideal gas law, PV = nRT.

### Step-by-Step Solution:

1. **Understand the Ideal Gas Law**: The ideal gas law states that PV = nRT, where P is pressure, V is volume, n is the number of moles, R is the ideal gas constant, and T is temperature in Kelvin.

2. **Graph Analysis**: We need to analyze the relationships depicted in the graphs:
- **Graph 1**: Pressure vs. Temperature (P-T graph)
- **Graph 2**: Volume vs. Temperature (V-T graph)
- **Graph 3**: Pressure vs. Volume (P-V graph)

3. **Graph 1 (P-T graph)**:
- For a fixed amount of gas, if the volume is held constant, increasing the temperature will increase the pressure. This graph should show a positive slope.
- If the graph shows a decreasing slope or negative correlation, it is incorrectly marked.

4. **Graph 2 (V-T graph)**:
- This graph represents the relationship between volume and temperature. If we consider the equation in terms of V and T, we can derive that volume increases with temperature at constant pressure.
- If the graph shows that volume decreases with increasing temperature, it is incorrectly marked.

5. **Graph 3 (P-V graph)**:
- According to Boyle's Law, for a fixed amount of gas at a constant temperature, pressure and volume are inversely related. If volume increases, pressure decreases, and vice versa. This graph should show a negative slope.
- If the graph incorrectly shows a positive slope, it is incorrectly marked.

6. **Determine Incorrectly Marked Graph**:
- After analyzing the graphs, if any graph shows a relationship that contradicts the established gas laws, that graph is incorrectly marked.
- Based on the analysis provided in the transcript, it was concluded that the volume-temperature graph (Graph 2) is incorrectly marked because it suggests that as volume decreases, temperature increases, which contradicts the ideal gas behavior.

### Conclusion:
The incorrectly marked graph is the one that shows the relationship between volume and temperature, indicating that volume decreases with increasing temperature.