Question

A wastewater sample has a temperature of 10 °C. The 5-day BOD (BOD) of the wastewater sample is determined as 120 mg/L at 10 °C, and the BOD decay constant (k) is known as 0.20 day 1 at 20°C. Calculate the BOD decay constant (k) at 10 °C.

Answer 1

Ans:) Given, At Temperature 100C - (BOD)5 = 120mg/L

Time = 5 days

Decay constant at 200C = 0.20 day-1

Basically BOD is the amount of oxygen in mg/L required to stabilize the water completely by means of the aerobic process.

The BOD equation is given as

$y=L(1-e^{-kt})$

where y =BOD consumed(mg/L)

L = The ultimate first stage BOD(mg/L)

k = Decay constant(day-1)

t = Time(day)

But we need to find the Decay constant at different temperatures. Which has no relation with the above equation because BOD is not depended on temperature, the decay constant depends on temperature with the expression:

$k_{1T} = k_{1-20^{0}C} * \Theta ^{T-20}$...................(1)

Where K1T = Decay constant at temperature T.

K1-200C = Decay constant at 200C

$\Theta = 1.047$ Temperature coefficient

From equation 1 we have-

..................(2)

Hence the Decay constant at 100C is 0.13 day-1.