Let's solve the problem step by step: --- ### **Step 1: Find the steady-state concentration in Tank 1** - **Inflow to Tank 1:** 10 L/min with concentration 0.3 kg/L. - **Outflow from Tank 1:** 10 L/min to Tank 2. - **Tank 1 volume:** 1000 L. At steady-state (\( t \to \infty \)), the amount of solute in Tank 1 doesn't change, so inflow of solute = outflow of solute. - **Inflow of solute to Tank 1:** \( 10 \text{ L/min} \times 0.3 \text{ kg/L} = 3 \text{ kg/min} \) - **Outflow of solute from Tank 1:** \( 10 \text{ L/min} \times C_1 \text{ kg/L} \), where \( C_1 \) is the steady-state concentration in Tank 1. Set inflow = outflow: \[ 3 = 10C_1 \implies C_1 = 0.3 \text{ kg/L} \] - **Total solute in Tank 1:** \( 1000 \text{ L} \times 0.3 \text{ kg/L} = 300 \text{ kg} \) **Explanation:** At steady state, the concentration in Tank 1 matches the input concentration, with the total solute being the product of volume and concentration. --- ### **Step 2: Find the steady-state concentration in Tank 2** - **Inflow to Tank 2:** All from Tank 1, 10 L/min with concentration \( C_1 = 0.3 \) kg/L. - **Additional inflow to Tank 2:** 10 L/min with concentration 0 kg/L (but since all flow into Tank 2 is from Tank 1, this is not relevant). - **Outflow from Tank 2:** 10 L/min. - **Tank 2 volume:** 1000 L. At steady-state, inflow of solute = outflow of solute. - **Inflow of solute to Tank 2:** \( 10 \text{ L/min} \times 0.3 \text{ kg/L} = 3 \text{ kg/min} \) - **Outflow of solute from Tank 2:** \( 10 \text{ L/min} \times C_2 \text{ kg/L} \), where \( C_2 \) is the steady-state concentration in Tank 2. Set inflow = outflow: \[ 3 = 10C_2 \implies C_2 = 0.3 \text{ kg/L} \] - **Total solute in Tank 2:** \( 1000 \text{ L} \times 0.3 \text{ kg/L} = 300 \text{ kg} \) **Explanation:** At steady state, the concentration in Tank 2 matches Tank 1 (since all solute comes from Tank 1). --- ## **Final Answer** - In the long run, **Tank 1 will have 300 kg of solute**. - In the long run, **Tank 2 will have 300 kg of solute**. This makes sense because both tanks are perfectly mixed, have the same inflow/outflow rates, and the input concentration to Tank 1 is 0.3 kg/L. Thus, both tanks reach the same steady-state concentration.