An insulated cylinder of volume 60 ~cm³$60 \mathrm{~cm}^3$ is filled with a gas at 27^$27^\circ\mathrm{C}$ and 2 atmospheric pressure. Then the gas is compressed making the final volume as 20 ~cm³$20 \mathrm{~cm}^3$ while allowing the temperature to rise to 77^$77^\circ\mathrm{C}$. The final pressure is ____ atmospheric pressure.

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