Question

The following graph represents the T-V curves of an ideal gas ( where T is the temperature and V the volume) at three pressures P₁, P₂ and P₃ compared with those of Charles's law represented as dotted lines.
 

Then the correct relation is :

• A. P₃ > P₂ > P₁
• B. P₁ > P₃ > P₂
• C. P₂ > P₁ > P₃
• D. P₁ > P₂ > P₃

Answer 1

The Correct Option is D

Step 1: Recall Charles’s Law 

Charles’s law states that at constant pressure, the volume of an ideal gas is directly proportional to its temperature:

$$ V \propto T \quad \text{(at constant P)} $$

Step 2: Analyze the Graph

In the Temperature-Volume (T-V) graph, the slope of each curve represents:

$$ \text{Slope} = \frac{1}{P} $$

Since pressure (P) is constant for a given curve, a steeper slope indicates a lower pressure.

Step 3: Compare the Slopes

\( P_1 \) has the least slope, indicating the highest pressure.

\( P_3 \) has the steepest slope, indicating the lowest pressure.

Step 4: Conclusion

The correct order of pressures is:

$$ P_1 > P_2 > P_3 $$

Answer 2

Step 1: Recall Charles’s Law 

Charles’s law states that at constant pressure, the volume of an ideal gas is directly proportional to its temperature:

$$ V \propto T \quad \text{(at constant P)} $$

Step 2: Analyze the Graph

In the Temperature-Volume (T-V) graph, the slope of each curve represents:

$$ \text{Slope} = \frac{1}{P} $$

Since pressure (P) is constant for a given curve, a steeper slope indicates a lower pressure.

Step 3: Compare the Slopes

• \( P_1 \) has the least slope, indicating the highest pressure.
• \( P_3 \) has the steepest slope, indicating the lowest pressure.

Step 4: Conclusion

The correct order of pressures is:

$$ P_1 > P_2 > P_3 $$