Problem $12$

Consider the P$-$V phase diagram for an unknown one$-$component

material as shown on right. Curve $\text{'}BCD\text{'},$ separating the liquid and

vapor regions, represents the boundary of the coexisting liquid and

vapor phases at equilibrium. Point $\text{'}C\text{'}$ is the critical point. Paths $\text{'}m-n-0-$

$p\text{'}$ and $\text{'}m-n-q\text{'}$ represent two separate isotherms obtained at the same

temperature in two separate experiments, respectively.

a$.$ Draw the corresponding P$-$T phase diagram for the above material,

and clearly show all curves and paths depicted here on the PV

diagram.

b$.$ Indicate $($approximately$)$ the region$($s$)$ for validity of ideal gas approximation in both the P$-$V and

P$-$T phase diagrams.

c$.$ Mention experimental conditions that will give the path $\text{'}$m$-$n$-$o$-$p$\text{'}$ and the path $\text{'}$m$-$n$-$q$\text{'},$

respectively.