Problem $2$

A wastewater treatment plant generates a large amount of sludge every day, which is considered as solid waste that needs to be treated. Incineration is one of the technologies commonly used to treat and manage sewage sludge if its energy content is acceptable. The sludge produced has a water content of $\backslash (80\backslash \%\backslash ).$ After dewatering, the sludge's water content is reduced to $\backslash (60\backslash \%\backslash ).$ The empirical formula of the dry mass of the sludge is $\backslash (\backslash$mathrm$\{$C$\}\_\{40\}\backslash$mathrm$\{$H$\}\_\{80\}\backslash$mathrm$\{$O$\}\_\{20\}\backslash$mathrm$\{$~N$\}\backslash ).$

$($i$)$ Calculate the percentage of carbon by dry mass in the sludge from the empirical formula. $(1$ mark$)$

$($ii$)$ Find the latent heat of water vapor released in $1$ kg of the sludge after dewatering. $(1$ mark$)$

$($iii$)$ Given that the typical High Heating Value $($HHV$)$ of the sludge is $\backslash (20,000\backslash$mathrm$\{$~kJ$\}/\backslash$mathrm$\{$kg$\}\backslash ),$ calculate the Low Heating Value $($LHV$)$ of the sludge to be incinerated. $(2$ marks$)$

Note: Molecular weight of elements: