The diagram below shows three continuous stirred tanks connected in series and initially

QUESTION:

The diagram below shows three continuous stirred tanks connected in series and initially filled with water.

The flow and mixing patterns in this system are studied by dissolving 1500 g of a salt (S) in the first tank, and then starting the 40 L/s flow through the system. Each tank outlet stream is monitored with an on-line thermal conductivity detector calibrated to provide instantaneous readings of salt concentration. The data are plotted versus time, and the results are compared with the plots that would be expected if the tanks are all perfectly mixed. Your job is to generate the latter plots.

(a) Assuming that pure water is fed to the first tank and that each tank is perfectly mixed (so that the salt concentration in a tank is uniform and equal to the concentration in the outlet stream from that tank), write salt balances on each of the three tanks, convert them to expressions for \(d C_{\mathrm{S} 1} / d t\), \(d C_{\mathrm{S} 2} / d t\), and \(d C_{\mathrm{S} 3} / d t\), and provide appropriate initial conditions.

(b) Without doing any calculations, on a single graph sketch the forms of the plots of \(C_{\mathrm{S} 1}\) versus t, \(C_{\mathrm{S} 2}\) versus t, and \(C_{\mathrm{S} 3}\) versus t you would expect to obtain. Briefly explain your reasoning.

(c) Use a differential equation-solving program to solve the three equations, proceeding to a time at which \(C_{\mathrm{S} 3}\) has fallen below 0.01 g/L, and plot the results.