The pressure and volume of an ideal gas are related as PV3/2 = K$PV^{3/2} = K$ (Constant). The work done when the gas is taken from state A (P₁, V₁, T₁$P_1, V_1, T_1$) to state B (P₂, V₂, T₂$P_2, V_2, T_2$) is:

Related Formula

PV = nRT$PV = nRT$

Core Logic

From the Ideal Gas Law:

In a V-T$V-T$ graph, the equation of the line represents y = mx$y = mx$, where the slope m$m$ is:

Thus, a higher slope corresponds to a lower pressure.

Step 2: Compare Slopes

From the given figure, the slope of line 2 is greater than the slope of line 1:

Therefore, inversely: P₂ < P₁$P_2 < P_1$ or P₁ > P₂$P_1 > P_2$.

Pattern Recognition

In V-T graphs, steeper lines mean lower Pressure. In P-T graphs, steeper lines mean lower Volume. It's an inverse inverse slope relationship.

Chapter Mix

Class 11 Physics: Thermodynamics