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In a city, the chemical formula of biodegradable fraction of municipal solid waste $\text{(MSW)}$ is $\text{C}_{100} \text{H}_{250} \text{O}_{80} \text{N}.$ The waste has to be treated by forced-aeration composting process for which air requirement has to be estimated.

Assume oxygen in air (by weight) $ = 23 \%,$ and density of air $ = 1.3 \; \text{kg/m}^{3}.$ Atomic mass: $\text{C = 12, H = 1, O = 16, N = 14.}$

$\text{C}$ and $\text{H}$ are oxidized completely whereas $\text{N}$ is converted only into $\text{NH}_{3}$ during oxidation.

For oxidative degradation of $1 \; \text{tonne}$ of the waste, the required theoretical volume of air (in $\text{m}^{3}/\text{tonne}$) will be (round off to the nearest integer)

  1. $4749$
  2. $8025$
  3. $1418$
  4. $1092$
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