A flue gas is cooled from $1050\backslash$deg C to $150\backslash$deg C$,$ and the heat is used to generate saturated steam at $100\backslash$deg C in a boiler. The flue gas has a heat capacity given by

CPR $=3\mathrm{.}83+0\mathrm{.}000551$ T$/$K

Water enters the boiler at $100\backslash$deg C and is vaporized at this temperature; its latent heat of vaporization is $2256\mathrm{.}9$ kJ$$kg$1.$ Take R $=8\mathrm{.}314$ J$$mol$1$K$1.$

With reference to a surroundings temperature of $25\backslash$deg C$,$ what is the lost work of this process in kJ$$mol$1$ of flue gas? $($You must provide an answer before moving to the next part.$)$

The lost work of this process is

kJ$$mol$1.$