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