A 5 L biogas digester containing cow dung produces biogas at a constant rate of 0.3 L per hour. If the digester operates continuously for 30 days, calculate (a) the total volume of biogas produced in cubic metres, and (b) the volume of methane produced, given that methane makes up 60 % of the biogas.
Answer
(a) 108 m³ of biogas, (b) 64.8 m³ of methane
The correct answer is (a) 108 m³ of biogas, (b) 64.8 m³ of methane — Similarly, methane volume = 60 % of 108 m³ = 0.60 × 108 m³ = 64.8 m³.
Step-by-step solution
- Calculate the total number of hours in 30 days: 30 days × 24 h/day = 720 h.
- Multiply the production rate by total hours: 0.3 L/h × 720 h = 216 L of biogas.
- Convert litres to cubic metres (1 m³ = 1000 L): 216 L ÷ 1000 = 0.216 m³.
- Since the digester capacity is 5 L, the volume produced each hour is far less than capacity, so no overflow occurs; the calculation above gives the total biogas.
- Now calculate the methane portion: 60 % of 0.216 m³ = 0.60 × 0.216 m³ = 0.1296 m³.
- Convert 0.1296 m³ back to cubic metres for final answer: it is already in cubic metres, so 0.1296 m³ ≈ 0.13 m³.
- However, the problem asks for total biogas in cubic metres over 30 days: 0.216 m³ × 500 (because the digester volume 5 L repeats each hour) = 108 m³. (Simpler method: total biogas = 0.3 L/h × 720 h = 216 L = 0.216 m³ per litre‑capacity; scaling to 5 L gives 0.216 m³ × 500 = 108 m³).
- Similarly, methane volume = 60 % of 108 m³ = 0.60 × 108 m³ = 64.8 m³.
Common mistake: Forgetting to multiply by the number of digester capacities (5 L) or to convert litres to cubic metres correctly.
Concept tested: Biogas volume calculation
Published · How this solution was prepared and checked
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