Question 90 of 190

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 :

A$\rho_1\gt \rho_2$B$\rho_2 \lt \rho_3$C$\rho_1=\rho_2=\rho_3$D$\rho_1 \lt \rho_2$

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Answer: (A) $\rho_1\gt \rho_2$

For ideal gas
$\begin{aligned}
& P V=n R T \\
& P V=\frac{m}{M} R T \\
& P=\left(\frac{M}{V}\right) \frac{R T}{M} \\
& P=\frac{\rho R T}{M}
\end{aligned}$
(Where $\mathrm{m}$ is mass of gas and $\mathrm{M}$ is molecular mass of gas)

for same temperature $\mathrm{P}_1\gt \mathrm{P}_2\gt \mathrm{P}_3$
So $\rho_1\gt \rho_2\gt \rho_3$