Home Work

$(1)$ A fluid is placed in a rigid container and spun as indicated in the figure below. The angular frequency of the rotation is $(ra\frac{d}{s}).$ The fluid fills the container and has no energy exchange with the surroundings. Gravity effect is negligible in this case.

$($a$)$ If the fluid contains more than one component, what conditions must the intensive thermodynamic properties satisfy in order for equilibrium to exist?

$($b$)$ The fluid is a dilute liquid solution of two components $($One is dissolved in the other$).$ Assume that the properties of the solute are independent of pressure. The total mole concentration $n=n_1+n_2=$ constant $($independent of $r).$ Find the mole concentration of the solute as a function of the radial distance, i$.$e$.,n_2=n_2(r).$