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:

For an ideal gas,

$$PV=nRT$$

Also density,

$$\rho=\frac{m}{V}$$

and

$$n=\frac{m}{M}$$

So ideal gas law becomes

$$P=\frac{\rho}{M}RT$$

or

$$P=\left(\frac{\rho R}{M}\right)T$$

This is the equation of a straight line in a P-T graph, whose slope is

$$slope=\frac{\rho R}{M}$$

Since R and molar mass M are constant, slope is directly proportional to density:

$$slope∝ρ$$

From the graph, line corresponding to $$\rho_1$$​ has greatest slope, then

$$\rho_2\ then\ \rho_3$$

Hence,

$$\rho_1>\rho_2>\rho_3$$