# Find the quantity Q(t) of salt in the tank?

• Math10
David are discussing how to solve a problem involving a tank and salt concentration.In summary, Chetan and David are discussing a problem involving a tank initially containing 40 gallons of pure water. They are trying to determine the quantity of salt in the tank at any given time, as well as the rate at which salt is entering and leaving the tank. They suggest setting up a differential equation and writing a balance of input - output = rate of accumulation to solve the problem.
Math10

## Homework Statement

A tank initially contains 40 gallons of pure water. A solution with 1 gram of salt per gallon of water is added to the tank at 3 gal/min, and the resulting solution dranes out at the same rate. Find the quantity Q(t) of salt in the tank at time t>0.

None.

## The Attempt at a Solution

I don't know how to set up the differential equation for this problem.

Let V be the volume of liquid in the tank in gal, q be the rate at which liquid is entering (and leaving) the tank in gal/min, and C(t) be the concentration of salt within the tank in gm/gal at time t. Based on this, at time t, how much salt is in the tank? If the tank is well mixed, what is the rate that salt is leaving the tank? What is the rate that salt is entering the tank? Write a balance of input - output = rate of accumulation.

Chet

## 1. How is the quantity of salt in the tank measured?

The quantity of salt in the tank is typically measured by taking a sample of the solution and analyzing it using a method such as titration or spectrophotometry.

## 2. What factors can affect the quantity of salt in the tank?

The quantity of salt in the tank can be affected by factors such as the initial concentration of salt in the solution, the rate of water flow in and out of the tank, and any addition or removal of salt from the tank.

## 3. How often should the quantity of salt in the tank be monitored?

The frequency of monitoring the quantity of salt in the tank will depend on the specific experiment or process being conducted. However, it is generally recommended to monitor the quantity at regular intervals to ensure accuracy and detect any changes.

## 4. Can the quantity of salt in the tank be adjusted?

Yes, the quantity of salt in the tank can be adjusted by adding or removing salt from the solution. This can be done manually or through automated systems, depending on the setup of the tank.

## 5. How is the quantity of salt in the tank related to other variables in the experiment?

The quantity of salt in the tank can be related to various other variables depending on the specific experiment. For example, it can be related to the concentration of other substances in the solution, the temperature of the tank, and the rate of reaction in certain chemical processes.

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