P-T diagram of an ideal gas having three different densities? (in three different cases) is shown in the figure. Which of the following is correct?

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Solution

Q.
P-T diagram of an ideal gas having three different densities $ρ_{1}, ρ_{2}, ρ_{3}$ (in three different cases) is shown in the figure. Which of the following is correct [2024]

1 $ρ_{1} > ρ_{2}$

2 $ρ_{2} > ρ_{3}$

3 $ρ_{1} < ρ_{2}$

4 $ρ_{1} = ρ_{2} = ρ_{3}$

Ans.
(1)

Ideal Gas Equation, $P V = n R T = \frac{m}{M} R T$

$P = (\frac{m}{V}) \frac{R T}{M} = ρ (\frac{R T}{M})$ (Where m is the mass of gas and M is the molecular mass of gas)

For the same temperature, $P_{1} > P_{2} > P_{3} ∴ ρ_{1} > ρ_{2} > ρ_{3}$

So, the correct answer is (1)

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