The BOD5 of a waste water is determined to be 240 mg/l at 20℃. The k value at 20℃ is known to be 0.23 day-1 . Calculate the BOD7 if the test were run at 10℃.

The BOD (Biochemical Oxygen Demand) is a measure of the amount of oxygen required by bacteria to decompose the organic matter in the water under aerobic conditions. The BOD5 is the BOD after 5 days, and the BOD7 is the BOD after 7 days.

The BOD at any time t can be calculated using the formula:

BODt = BODu * (1 - e^-kt)

where:

• BODt is the BOD at time t,
• BODu is the ultimate BOD (the BOD after an infinite amount of time),
• k is the deoxygenation rate constant, and
• t is the time.

The BOD5 at 20℃ is given as 240 mg/l, and the k value at 20℃ is given as 0.23 day-1.

First, we need to calculate the ultimate BOD (BODu) using the BOD5 and the k value at 20℃. Rearranging the formula for BODt gives:

BODu = BOD5 / (1 - e^-k*5)

Substituting