P-T diagram of an ideal gas having three different densities ρ₁, ρ₂, ρ₃ (in three different cases) is shown in the figure. Which of the following is correct: (a) ρ₁ > ρ₂ (b) ρ₂ < ρ₃ (c) ρ₁ = ρ₂ = ρ₃ (d) ρ₁ < ρ₂

Answer: (a). P = (ρ R T)/(M), so for a fixed density the P - T graph is a straight line of slope (ρ R)/(M). Slope ∝ ρ: the steepest line has the largest density. From the figure, slope of ρ₁ > slope of ρ₂ > slope of ρ₃, so ρ₁ > ρ₂ > ρ₃. So the answer is (a) ρ₁ > ρ₂.

P-T diagram of an ideal gas having three different densities ρ₁, ρ₂… | JEE Main 2024 (4 Apr, Shift 1)

Q35JEE Main 2024 · 4 APR · SHIFT 1Medium

Gas Laws & Ideal Gas Equation

P-T diagram of an ideal gas having three different densities $\rho_1, \rho_2, \rho_3$ (in three different cases) is shown in the figure. Which of the following is correct:

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Answer: (a)

$P = \frac{\rho R T}{M}$ , so for a fixed density the $P$ - $T$ graph is a straight line of slope $\frac{\rho R}{M}$ .
Slope $\propto \rho$ : the steepest line has the largest density.
From the figure, slope of $\rho_1$ > slope of $\rho_2$ > slope of $\rho_3$ , so $\rho_1 > \rho_2 > \rho_3$ .
So the answer is (a) $\rho_1 > \rho_2$ .

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