A 10 L biogas digester receives cow dung and produces biogas at a constant rate of 0.4 L per hour. The digester runs continuously for 20 days. (a) What is the total volume of biogas produced in cubic metres? (b) If biogas contains 60 % methane, how many cubic metres of methane are produced? (c) Given the calorific value of methane is 55.5 kJ per litre, estimate the total energy produced in megajoules.
Answer
0.192 m³, 0.115 m³, 10.7 MJ
The correct answer is 0.192 m³, 0.115 m³, 10.7 MJ — Convert to MJ: 10 656 kJ ÷ 1000 = 10.656 MJ ≈ 10.7 MJ.
Step-by-step solution
- Total time = 20 days × 24 h/day = 480 h.
- Biogas produced = 0.4 L/h × 480 h = 192 L.
- Convert to cubic metres: 192 L ÷ 1000 = 0.192 m³.
- Methane volume = 60 % of 0.192 m³ = 0.115 m³.
- Energy in kJ = 192 L × 55.5 kJ/L = 10 656 kJ.
- Convert to MJ: 10 656 kJ ÷ 1000 = 10.656 MJ ≈ 10.7 MJ.
Common mistake: Converting litres to cubic metres incorrectly or ignoring percentage of methane
Concept tested: Biogas production and energy estimation
Published · How this solution was prepared and checked
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