A mixture of decomposable solid waste having chemical formula as C$136$H$222$O$100$N$2$ is sent for anaerobic digester for biogas generation. Using $1$ kg of solid waste as a basis, determine the volume of methane and carbon dioxide generated. The specific weight of methane $($CH$4)$ and CO$2$ are $1\mathrm{.}395$ m$3/$kg and $0\mathrm{.}505$ m$3/$kg$,$ respectively. Atomic weight $($unit $=$ kg$/$k$-$mole$)$ of C$,$ H$,$ O and N are $12,1,16,$ and $14,$ respectively. Anaerobic digestion reaction is given:$C_a{H}_b{O}_c{N}_d+(\frac{4a-b-2c+3d}{4})H_{2}O$

$(\frac{4a+b-2c-3d}{8})C{H}_4+(\frac{4a-b+2c+3d}{8})C{O}_2+dN{H}_3$