1. A tank initially contains 200liters of fresh water. Brine containing 2N/L dissolved salt enters the tank?

Question

at 5L/MIN and the resulting mixture leave the tank at the same rate. Find the salt concentration in the tank after 5 mins.

2. A storage battery discharge is reduced to 50% of its original value at the end of 2days, how long will it take to reduce the charge of 25% of its original value.

Answer 1

both of these are of the variety "change = incoming - outgoing"

#1. S = salt{ in N } in tank at time t...dS / dt = 2{N/L} 5{L/min} - ( S / 200) {N/L} 5{L/min}= 10 - S / 40---> S ' + (1/ 40) S = 10...1st order..solve..S(0) = 0

#2. C = charge.....dC /dt = 0 - k C, C(0) = 1 , C(2) = 1/2...trivial to solve, an exponential...you do the work