A tank contains 80 kg of salt and 1000 L of water. A...

A tank contains 80 kg of salt and 1000 L of water. A solution of a concentration 0.04 kg of salt per liter enters a tank at the rate 9 L/min. The solution is mixed and drains from the tank at the same rate. a.) What is the concentration of our solution in the tank initially? concentration = 80/1000 (kg/L) b.) Find the amount of salt in the tank after 1.5 hours. amount = .04 (kg) c.) Find the concentration of salt in the solution in the tank as time approaches infinity. concentration = 0.04 (kg/L)

Labs

Want to see this concept in action?

NEW

Explore this concept interactively to see how it behaves as you change inputs.

View Labs

Transcript

00:01 Okay, so we have a tank containing 80 kilograms of salt and 1 ,000 liters of water.

00:06 We have the initial concentration that's entering the tank that's given to us.

00:12 So now let's just determine kind of the differential equation that governs this.

00:18 So we have dqdt equals the rate in minus the rate out.

00:22 The rate in we see is going to be the 0 .04 kilograms per liter entering.

00:31 At a rate of 9 liters per minute.

00:35 And then exiting, it's going to be whatever the amount, q of t, kilograms is in the system, over the number of liters of water, so that's going to be 1 ,000 liters.

00:49 And then the rate at which it's leaving is the same, so it's 9 liters per minute.

00:55 So then combining all this, we have 0 .04 times 9.

01:01 With 0 .36.

01:03 So we have dqdt equals 0 .36 minus 9 over 1 ,000.

01:12 So we could just write that as 0 .009, so 0 .009, q of t.

01:21 Now we see that this is a constant coefficient, so we can write that our a value is a negative 0 .009, and our b value is a negative 0 .36.

01:31 So then we can write q as being equal to b over a.

01:36 So it's going to be 0 .36 divided by 0 .009.

01:42 So that's 40 plus c .e to the a .t.

01:49 So negative 0 .009t.

01:52 And then we know that initially it contains 80 kilograms of salt.

01:55 So q of 0 is going to equal 40 plus c...

Question

Please give Ace some feedback