Please explain thanks A tank, containing 900 liters of liquid, has a brine solut

Question

Please explain thanks A tank, containing 900 liters of liquid, has a brine solution entering at a constant rate of 4 liters per minute. The well-stirred solution leaves the tank at the same rate. The concentration within the tank is monitored and found to be c(t) = e^-t/500/20 kg/L Determine the amount of salt initially present within the tank. Initial amount of salt = Determine the inflow concentration C_in (t), where C_in (t) denotes the concentration of salt in the brine solution flowing into the tank. c_in (t) =

Explanation / Answer

a)

Initially we could use the C(t), therefore

t = 0, then

C(t = 0) = exp(-0/500) / 50 = 1/50 = 0.02 kg/L

b)

Cin(t) denoting concentration of salt in brine solutino

We could assume that the final concentration will be equal than that of the inlet concentration

so

assume a very high T, i.e. infinity

exo(-inifinite/500) --> Exp(-infinite) --> 0

The Concentration will be 0 according to the equation

that is, there is only water in solution

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