Example $7,15,1.$ The following data are given for a family bigas digester suifable for the output of five cows : the reten tion time is $20$ days, temperature $30C,$ dry matter consumed per day $=2kg,$ biogas yield is $0\mathrm{.}24m^3$ per $kg.$ The efficiency of burner is $60\%,$ methane proportion is $0\mathrm{.}8.$ Heat of combustion of methane $=28M\frac{J}{m^3}.$

Calculate: $($i$)$ the volume of biogas digester, and

$($ii$)$ the power available from the digester.