Question

Pressure versus temperature graph of an ideal gas of equal number of moles of different volumes are plotted as shown in figure. Choose the correct alternative.

• A. $V_1 = V_2 = V_3 = V_4$
• B. $V_4 > V_3 > V_2 > V_1$
• C. $V_1 = V_2$; $V_3 = V_4$ and $V_2 > V_3$
• D. $V_1 = V_2$, $V_3 = V_4$ and $V_2 < V_3$

Answer 1

Answer: (C)

As $P-T$ graphs are straight lines, passing through origin, therefore, $P\,\propto \,T$. But as $P = \left(\frac{\mu R}{V}\right)T$, therefore, the slope of straight line $\propto \frac{1}{V}$
As $\left(Slope\right)_{12 } < \left(Slope\right)_{34}\quad\therefore \quad V_{2} > V_{3}$
As for a given slope, $V$ is constant, therefore,
$V_{1} = V_{2}$ and $V_{3} = V_{4}$.