Q$1$: $[25$ marks$]$

A classroom has the dimensions of $10$ m long, $8$ m wide and $6$ m high and an open window of $1\mathrm{.}5$ m long and $2$ m high. A methanol bottle breaks to form a $\backslash (2-\backslash$mathrm$\{$m$\}\backslash )$ diameter pool fire. The initial room temperature is $\backslash (20^\{\backslash$circ$\}\backslash$mathrm$\{$C$\}\backslash ),$ and the heat of combustion of methanol or wood is $\backslash (22\backslash$mathrm$\{$MJ$\}/\backslash$mathrm$\{$kg$\}\backslash ),$

$($a$)$ What is the heat release rate of the pool fire?

$(5$ marks$)$

$($b$)$ Can this pool fire always trigger the heat detector $($RTI $\backslash (=120\backslash$mathrm$\{$~m$\}^\{1/\backslash$mathrm$\{$s$\}^\{1/2\}\}\backslash ))$ with a threshold temperature of $\backslash (65^\{\backslash$circ$\}\backslash$mathrm$\{$C$\}\backslash )?$

$(6$ marks$)$

$($c$)$ If this fire is $1$ m away from the detector, how long it triggers the heat detector? $(7$ marks$)$

$($d$)$ If there are twenty $\backslash (25-\backslash$mathrm$\{$kg$\}\backslash )$ sofas in the room, and flashover occurs in $5$ min $,$ what is the total burning duration?

$(7$ marks$)$