When a sample of ideal gas is changed from an initial state to a final state, various curves can be plotted for the process like P-V curve, V-T curve,P-T curve etc.
For example, P-V curve for a fixed amount of an ideal gas at constant temperature is a rectangular hyperbola, V-T curve for a fixed amount of an ideal gas at constant volume is again a straight line. However, the shapes may vary if the constant parameters are also changed.
Now, answer the following questions :
Which of the following graphs is not possible for a fixed amount of ideal gas upon moving from initial state A to final state B :

Options

A.
B.
C.
D. None of these

Explanation

To determine which graph is not possible for a fixed amount of ideal gas moving from initial state A to final state B, we need to analyze the given graphs based on the properties of ideal gases and the relationships between pressure (P), volume (V), and temperature (T).

### Step-by-Step Solution:

1. **Understanding Ideal Gas Behavior**:
- For a fixed amount of ideal gas, the number of moles (n) remains constant. The relationships between P, V, and T are described by the ideal gas law:
\[ PV = nRT \]
- This means that if any two of the variables (P, V, T) are known, the third can be determined.

2. **Analyzing the First Graph**:
- The first graph is a P-V curve at constant temperature. According to Boyle's Law, for a fixed amount of gas at constant temperature, the graph of P vs. V is a rectangular hyperbola.
- As we move from state A to state B, if pressure increases, volume must decrease to maintain the product PV constant.
- **Conclusion**: This graph is possible.

3. **Analyzing the Second Graph**:
- The second graph shows a linear increase in pressure with volume. This can occur if the temperature is increasing.
- If temperature increases, the relationship can be linear under certain conditions, as described by the ideal gas law.
- **Conclusion**: This graph is also possible.

4. **Analyzing the Third Graph**:
- The third graph is a V-T curve, where V is constant. This indicates that the volume does not change while the temperature changes.
- According to the ideal gas law, if V is constant, then as temperature increases, pressure must also increase proportionally.
- This graph is also valid as it can represent a scenario where volume remains constant while temperature changes.
- **Conclusion**: This graph is possible.

5. **Final Analysis**:
- Since all three graphs analyzed (P-V, P-T, and V-T) are possible for a fixed amount of ideal gas transitioning from state A to state B, we conclude that none of the graphs presented are impossible.
- Therefore, the answer to the question is that all graphs are possible.

### Final Answer:
None of these graphs is impossible for a fixed amount of ideal gas moving from initial state A to final state B.