Q$4($a$)$ Ethane is fed to a boiler where it is burnt with $45\%$ excess air. The ethane is supplied to the boiler at $25C$ and the combustion air at $55C.$ The boiler stack temperature is measured at $120C.$ The boiler is used to evaporate condensate at $100C$ to steam at $100C.$

Assuming that there are no other heat losses, determine the mass of steam produced.

$C_p(O_2)=30\frac{J}{m}ol.C$

$C_p(N_2)=30\frac{J}{m}ol.C$

$C_p(H_{2}O)=35\frac{J}{m}ol.C$

$C_p(C{O}_2)=39\frac{J}{m}ol.C$

Latent heat of vaporization of water at $100C=2257k\frac{J}{k}g.$

Heat of combustion of ethane at $25C$ is $-1428k\frac{J}{m}ol,$ the heat of combustion refers to each mole of fuel burnt with the standard state of reactant and products as gas. Air consists of $21\%O_2$ and $79\%N_2$ on a volume basis.

$[20$ marks$]$

$($b$)$ Describe, with the aid of a clearly labeled diagram, the enthalpy with phase change including the latent heat of fusion and the latent heat of vaporization.

$[5$ marks$]$