Question $1[40$ marks $]$

An industrial boiler is rated at $100MW,$ meaning it converts chemical energy to thermal energy at a

rate of $100MW.$ It burns natural gas $($NG$),$ modelled as methane $(C{H}_4),$ in air. You may assume that

all species in this question can be modelled as ideal gases.

$($a$)$ Calculate the mass flow rate of in $\{$:$k\frac{g}{s})$ required to deliver $100MW.$

$($b$)$ Calculate the volume flow rate of $C{H}_4$ at standard temperature and pressure $($STP$)$ in

units of $\frac{m^3}{s})$ required to deliver $100MW.$ STP corresponds to $0C$ and $101$kPa. Recall that the

fuel can be modelled as an ideal gas.

$($c$)$ To reduce $C{O}_2$ emissions, the fuel is switched to a $50$:$50($by volume or mole$)C{H}_4$:$H_2$ mixture.

If the total volume flow rate of fuel is unchanged from part $($b$),$ calculate the rate of release of

thermal energy $(Q^{}$ in MW$)$ for the boiler burning the $C{H}_4$:$H_2$ mixture.

$($d$)$ Calculate the $C{O}_2$ emission factor of the $C{H}_4$:$H_2$ mixture $(E_{C{H}_4\text{:}{H}_2}$ in $gC\frac{O_2}{M}J).$

Table Q$1$: Useful properties