JEE Main · 2022 · 27 Jun 2022 · Shift 2 · States of Matter

Which amongst the given plots is the correct plot for pressure (p) vs density (d) for an ideal gas ?

(A)(see structure)
(B) $T_{3} > T_{2} > T_{1}$ (see structure)
✓ Correct
(C) $T_{3} > T_{2} > T_{1}$ (see structure)
(D) $T_{3} > T_{2} > T_{1}$ (see structure)

Answer: (B)

Solution

For an ideal gas, the ideal gas equation is

P V = n R T

. Rearranging in terms of density

d = \frac{m}{V} = \frac{n M}{V}

, we get

P = \frac{R T}{M} d

. This shows that pressure is directly proportional to density at constant temperature, with slope

\frac{R T}{M}

. Since the slope increases with temperature, higher temperature lines have steeper slopes. The correct plot shows straight lines passing through the origin with increasing slopes for

T_{3} > T_{2} > T_{1}

JEE Main · 2022 · 27 Jun 2022 · Shift 2 · Single correct option

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