The BOD of the sewage is calculated as follows:
BOD (mg/L) = 77 g/day * 1000 mg/g / 180 L/day = 428 mg/L
This means that the sewage contains 428 mg of BOD per liter.
The amount of oxygen that needs to be added to the water is calculated as follows:
Oxygen needed (kg/day) = BOD (mg/L) * Total volume of water (L) / 1000 kg/L = 428 mg/L * 500,000 L / 1000 kg/L = 235 kg/day
This means that 235 kg of oxygen needs to be added to the water every day to keep the BOD at a safe level.
Therefore, the BOD of the sewage is 428 mg/L, and the amount of oxygen that needs to be added to the water is 235 kg/day.