A plant is under shutdown and a tank with a capacity of $12,000m^3$ is to be inspected. This requires

technicians to enter the tank. Prior to the entry, the tank is emptied and is at atmospheric

conditions which is $1$atm pressure and $25C.$ The safety engineer measures the composition

inside the tank and determines that the tank contains $10$mol$\%$ of a toxic contaminant and the

rest being air. In order to facilitate the inspection, the plant manager brings a blower that can

supply air at $100mo\frac{l}{s}$ to purge the tank of the contaminant. The setup is shown in the figure

below.

Useful Info: Gas constant, $R=8\mathrm{.}2{10}^{-5}{m}^{3}at\frac{m}{K}.$mol

a$)$ Based on the information given, and stating the assumptions you would make, derive

a transient mass balance that describes the change in the contaminant composition

within the tank with time. $[5$ MARKS$]$

b$)$ BONUS: Regulations require that contaminant composition is below $100$ ppm for safe

entry. Calculate the time required to achieve safe limits$.[5$ MARKS$]$