$5\mathrm{.}48.$ A flue gas is cooled from $2000$ to $300(F),$ and the heat is used to generate saturated

steam at $212(F)$ in a boiler. The flue gas has a heat capacity given by:

$\frac{C_P}{R}=3\mathrm{.}83+0\mathrm{.}000306\frac{T}{R}$

Water enters the boiler at $212(F)$ and is vaporized at this temperature; its latent heat

of vaporization is $970\mathrm{.}3(Btu)(l{b}_m{)}^{-1}.$

$($a$)$ With reference to a surroundings temperature of $70(F),$ what is the lost work of

this process in $(Btu)(lb$ mole ${)}^{-1}$ of flue gas?

$($b$)$ With reference to a surroundings temperature of $70(F),$ what is the maximum

work, in $($Btu$)($lb mole