Question

5. (20 points) A tank with a capacity of 500 liters contains 200 liters of water with 100 grams of a material in solution. Water containing a concentration of 1 g/liter of the material enters the tank at a rate of 3 liters/min, and the well-stirred mixture leaves the tank at a rate of 2 liters/min. Find the amount of mass of the material in the tank at any given time t prior to when the tank begins to overflow.

Answer 1

soolt 1914 Tzulmin 2oolt 100gm 3Lt/min ut ult) is volutne of tark at timet, and mct) û mass of martua at time to vit) = 3-2 =) V! (+-) = 1 =) V!!)=Wurt mict) = (1)13) - 2 m(t); 510)=100, VIE) V(1-) = 200++ i ost £300, milt) = 3 - 2m(t) ; m (o)=100 - 2004 t (200++) micr) + 2 mln) = 3(20045) (200++)? m'(t) + 2(2007b) m(t)=3(2004)" d [200+time+) = 3(200++)2 (200++?m (H) = | 31200++)2 dt (200+ t’m (H) = (200+673 +C. m(H) = (200++) + c . (2007) mio) = 200 + 6oiR = 100 c=-481046 m(t) = 1200++) - 4X10% (200+4) = (200++) - (200tt ) m(t) = 200 +t - 200012 200tt |m(300)= 484 gm