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A very large tank contains 10 liters of pure water. Salt solution (20 g/l) is pumped into the tank at 2 liter per minute. The salt concentration in g/l in the tank after a very long time will be
- a)5
- b)10
- c)20
- d)40
Correct answer is option 'C'. Can you explain this answer?
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A very large tank contains 10 liters of pure water. Salt solution (20 ...
Given:
- Volume of the tank = 10 liters
- Concentration of salt solution = 20 g/l
- Rate at which salt solution is pumped into the tank = 2 liters per minute
To find:
The salt concentration in g/l in the tank after a very long time.
Solution:
To find the salt concentration in the tank after a very long time, we need to consider the amount of salt being added and the volume of water in the tank.
1. Amount of salt being added per minute:
The concentration of salt solution is given as 20 g/l. So, for every liter of solution being pumped into the tank, 20 grams of salt is being added.
Since the rate at which the solution is being pumped into the tank is 2 liters per minute, the amount of salt being added per minute = 20 g/l * 2 l/min = 40 g/min.
2. Volume of water in the tank:
The tank initially contains 10 liters of pure water. As the salt solution is being pumped into the tank, the volume of water in the tank will increase.
Since the rate at which the solution is being pumped into the tank is 2 liters per minute, the volume of water in the tank after 't' minutes can be given by:
Volume of water = 10 liters + 2 liters/min * t
3. Salt concentration in the tank after 't' minutes:
The total amount of salt in the tank after 't' minutes will be the sum of the initial amount of salt and the amount of salt being added per minute multiplied by 't'.
Total amount of salt = 0 g + 40 g/min * t
The volume of water in the tank after 't' minutes is given by: Volume of water = 10 liters + 2 liters/min * t
Therefore, the salt concentration in the tank after 't' minutes can be given by:
Salt concentration = Total amount of salt / Volume of water
Salt concentration = (40 g/min * t) / (10 liters + 2 liters/min * t)
As 't' approaches infinity (a very long time), the volume of water in the tank will continue to increase, while the amount of salt being added per minute will remain constant. Therefore, the salt concentration in the tank will approach a constant value.
Hence, the correct answer is option 'c' (20 g/l).
- Volume of the tank = 10 liters
- Concentration of salt solution = 20 g/l
- Rate at which salt solution is pumped into the tank = 2 liters per minute
To find:
The salt concentration in g/l in the tank after a very long time.
Solution:
To find the salt concentration in the tank after a very long time, we need to consider the amount of salt being added and the volume of water in the tank.
1. Amount of salt being added per minute:
The concentration of salt solution is given as 20 g/l. So, for every liter of solution being pumped into the tank, 20 grams of salt is being added.
Since the rate at which the solution is being pumped into the tank is 2 liters per minute, the amount of salt being added per minute = 20 g/l * 2 l/min = 40 g/min.
2. Volume of water in the tank:
The tank initially contains 10 liters of pure water. As the salt solution is being pumped into the tank, the volume of water in the tank will increase.
Since the rate at which the solution is being pumped into the tank is 2 liters per minute, the volume of water in the tank after 't' minutes can be given by:
Volume of water = 10 liters + 2 liters/min * t
3. Salt concentration in the tank after 't' minutes:
The total amount of salt in the tank after 't' minutes will be the sum of the initial amount of salt and the amount of salt being added per minute multiplied by 't'.
Total amount of salt = 0 g + 40 g/min * t
The volume of water in the tank after 't' minutes is given by: Volume of water = 10 liters + 2 liters/min * t
Therefore, the salt concentration in the tank after 't' minutes can be given by:
Salt concentration = Total amount of salt / Volume of water
Salt concentration = (40 g/min * t) / (10 liters + 2 liters/min * t)
As 't' approaches infinity (a very long time), the volume of water in the tank will continue to increase, while the amount of salt being added per minute will remain constant. Therefore, the salt concentration in the tank will approach a constant value.
Hence, the correct answer is option 'c' (20 g/l).
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A very large tank contains 10 liters of pure water. Salt solution (20 g/l) is pumped into the tank at 2liter per minute. The salt concentration in g/l in the tank after a very long time will bea)5b)10c)20d)40Correct answer is option 'C'. Can you explain this answer?
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