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 :

Question

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Answer 1

Step 1: State Charles's Law

Charles's law dictates that at a constant pressure, the volume of an ideal gas is directly proportional to its absolute temperature:

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

Step 2: Interpret the Graph

The slope of each curve in the Temperature-Volume (T-V) graph is defined as:

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

For a specific curve, pressure (P) is held constant. Therefore, a steeper slope signifies a lower pressure.

Step 3: Evaluate Slopes

$ P_1 $ exhibits the smallest slope, implying the highest pressure.

$ P_3 $ exhibits the steepest slope, implying the lowest pressure.

Step 4: Final Determination

The pressures are ordered as follows:

$$ P_1 > P_2 > P_3 $$

The Correct Option is D