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A very large tank initially contains 100 kg of 60% brine (60 wt% salt in water). at the start of a process, an inlet stream of 10 kg/min of a 10% brine solution begins flowing into the tank. solution also begins to drain out of the tank at a rate of 15 kg/min. assume complete mixing. calculate the mass of salt (in kg) in the tank after 10 minutes salt in the tank = kg

User S Panfilov
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Final answer:

The mass of salt in the tank after 10 minutes would be 61 kg.

Step-by-step explanation:

To calculate the mass of salt in the tank after 10 minutes, we need to consider the inflow and outflow of salt in the tank. The inflow rate is 10 kg/min of a 10% brine solution, which means it contains 10% salt by mass. Therefore, the inflow of salt is 10 kg/min × 0.10 = 1 kg/min. The outflow rate is 15 kg/min, but we need to determine the percentage of salt in the tank at each moment to calculate the outflow of salt. Since the tank initially contains 100 kg of 60% brine solution, it contains 100 kg × 0.60 = 60 kg of salt. After 10 minutes, the inflow of salt would be 1 kg/min × 10 min = 10 kg. The outflow of salt would be (15 kg/min × 10 min) × (60 kg / (100 kg + 10 kg)) = 9 kg. Therefore, the mass of salt in the tank after 10 minutes would be 60 kg + 10 kg - 9 kg = 61 kg.

User Stephenbayer
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Answer:To solve this problem, let's calculate the mass of salt in the tank after 10 minutes.

We can break down the problem into two parts: the salt that was initially in the tank and the salt that entered or left the tank during the 10 minutes.

Salt initially in the tank:

The initial mass of salt in the tank is 100 kg multiplied by the concentration of salt in the brine, which is 60% or 0.6.

Initial salt in the tank = 100 kg * 0.6 = 60 kg.

Salt entering the tank:

The inlet stream brings in 10 kg/min of a 10% brine solution. We need to calculate the mass of salt in this stream.

Salt entering the tank per minute = 10 kg * 0.1 = 1 kg/min.

Since the inlet stream flows for 10 minutes, the total mass of salt entering the tank during this period is:

Salt entering the tank = 1 kg/min * 10 min = 10 kg.

Salt leaving the tank:

The drain stream removes 15 kg/min from the tank. However, since the concentration of salt in the tank is not specified, we can assume that the concentration of salt in the drain stream is the same as the concentration of the tank's contents.

Salt leaving the tank per minute = Concentration of salt in the tank * Drain stream rate = 0.6 * 15 kg/min = 9 kg/min.

Since the drain stream also operates for 10 minutes, the total mass of salt leaving the tank during this period is:

Salt leaving the tank = 9 kg/min * 10 min = 90 kg.

Calculation of final salt mass:

To find the final mass of salt in the tank after 10 minutes, we need to add the initial salt in the tank, the salt entering the tank, and subtract the salt leaving the tank.

Final salt in the tank = Initial salt in the tank + Salt entering the tank - Salt leaving the tank

Final salt in the tank = 60 kg + 10 kg - 90 kg

Final salt in the tank = -20 kg.

The result, -20 kg, indicates that the tank has a deficit of 20 kg of salt after 10 minutes, which means there is not enough salt to maintain the specified concentrations.

Step-by-step explanation:

User Roberto Alsina
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