Question

A brine solution of salt flows at a constant rate of 9 L/min into a large tank that initially held 100 L of brine solution in which was dissolved 0.2 kg of salt. The solution inside the tank is kept well stirred and flows out of the tank at the same rate. If the concentration of salt in the brine entering the tank is 0.04 kg/L, determine the mass of salt in the tank after t min. When will the concentration of salt in the tank reach 0.01 kg/L?

Answer 1

Solutiorn Let χ(e) be the mass of Solt 'n ktiorams, ie.ǐn the tonk ot time t) Since the tanks nitialy flted uith Poesh watea we knthoxo In ozdex to de teamene χ(t),ur will use whal we know about bhequju, rte at which χ(t) charges over o Lime, uhắch is x'(b) an expre ssion r0า χ(t). fin expression for x'(t) ust be given as the ซ0te of Salt entes be tank. minuts the aate alt Reaves the tank Cin kiton* Fes nu TD do this we ineed Lo knc the volume of Soluionn the tank at- e K volume op Solut ion in the tank met The. volume. İS91 vento be 100L qL of tquad enieas the tonk and same leaves with ecach minute we can See thatat time ) the votume of Solution nthe tank must e 100F Oow, the salt enteaing the ank is easily Reckoned: q litea of baine s enteai these's o oy kgof Soltr*3 litea, and So thae ams giuen to be oo ialy ard since al time Pea minte

minute a -otal of 36 KgofSolts theae s ate of tleaves t xl Kg of Solution Salt on the tank. (unifbsmlu dissol dissolved ghothe (oo +L) to gve a coce.ntacion of es fSoluiontogva ite Since, letes of Solution ig teaving of Salt Pea ue conclude: 92CL) kg of Solt s eaving pe inuue folles χ|(t) the of Jozi v oki ve as x!(b)こ(Rate of Salt cnteas tonk)-(rate of Solt leaves tank 160 E) he diffexentiaeation is: t- at oott) qd는 100 loo)

9 100 t) and the mass at time (t) is, the concentration a上the ernet- v(t) 10 100十七) whan 26 l0 oot 3,.Goo