Final answer:
To find the time it takes for the dye concentration in the tank to reach 1% of its original value, we can use the concept of dilution. By applying the dilution formula, we can calculate that it would take approximately 166.67 hours for the concentration to reduce to 1% of its original value.
Step-by-step explanation:
To find the time that will elapse before the concentration of dye in the tank reaches 1% of its original value, we can use the concept of dilution. The tank is being rinsed with fresh water flowing in at a rate of 2 L/min, and the well-stirred solution is flowing out at the same rate.
The concentration of dye in the tank after a certain amount of time can be calculated using the formula:
C1V1 = C2V2
Where:
- C1 = initial concentration of dye (1 g/L)
- V1 = volume of dye solution (200 L)
- C2 = final concentration of dye (1% of the original value, which is 0.01 g/L)
- V2 = volume of water rinsed through the tank (unknown)
Rearranging the formula to solve for V2:
V2 = (C1V1) / C2 = (1 g/L × 200 L) / (0.01 g/L) = 20000 L
So, it would take 20000 L / 2 L/min = 10000 min = 166.67 hours for the concentration of dye in the tank to reach 1% of its original value.