P-T diagram of an ideal gas having three different densities $\rho_1, \rho_2, \rho_3$ (in three different…
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 :
$\rho_1>\rho_2$
$\rho_2 < \rho_3$
$\rho_1=\rho_2=\rho_3$
$\rho_1 < \rho_2$
Solution
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 $\mathrm{P}_1>\mathrm{P}_2>\mathrm{P}_3$
So $\rho_1>\rho_2>\rho_3$
