Liquid hazardous wastes are blended in a CSTR to maintain a minimum energy content before burning them in a hazardous waste incinerator. The energy content of the waste currently being fed is 8.0 MJ/kg (mega- joules/kilogram). A new waste is injected in the flow line into the CSTR. It has an energy content of 10.0 MJ/kg. If the flow rate into and out of the 0.20 m3 CSTR is 4.0 L/s, how long will it take the effluent from the CSTR to reach an energy content of 9 MJ/kg?

    t = 25 s

Explanation:

Let's analyze this exercise, the energy of each matter is 8 and 10 Mj / kg, it asks us that the container have an average energy of 9 MJ, this energy must be

         9 m = 8 m₁ + 10 m₂

          If m = m₁ + m₂ = 2m’

         m’= m / 2

Each liquid must contribute the same amount of mass, so that the average energy is 9 MJ

The flow rate is defined as the amount of liquid per time unit

         Q = V / t

         t = V / Q

The expression for density is

       ρ = m / V

       m = ρ V

Suppose the two liquids have the same density, they are dissolved in the same amount of water, we see that the liquids must fill a volume of half the container,

           V' = V₀ / 2

            V' = 0.2 / 2 = 0.1 m3

Let's reduce the magnitude to the SI system

          Q = 4 .0 L / s (1 m³ / 1000 L) = 4.0 10⁻³ m³ / s

Let's calculate  

           t = 0.1 / 4.0 10⁻³

          t = 25 s

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