We wish to consider the work that can be obtained by carrying out the following reactions in a steadyflow process:

$H_{2(g)}+\frac{1}{2}{O}_{2(g)}{H}_2{O}_{(l)}$

$H_{2(g)}+\frac{1}{2}{O}_{2(g)}{H}_2{O}_{(g)}$

Hydrogen is burned completely with the theoretical amount of air, both initially at $101\mathrm{.}325$kPa and $300K,$ in an adiabatic reactor at constant pressure. If the flue gases are cooled to $500K$ at a constant pressure of $101\mathrm{.}325$kPa by the transfer of heat to a boiler to generate superheated steam at $3\mathrm{.}5$MPa and $540C,$ what is the work that will be obtained from a simple power$-$plant cycle operating as follows?

A turbine $)=(80\%$ expands the steam from the boiler to $0\mathrm{.}014$MPa. A condenser at $0\mathrm{.}014$MPa delivers saturated liquid water to a pump $)=(80\%$ that returns the water to the boiler. The total enthalpy and entropy changes for the reversible cooling of flue gases to $500K$ are $H=-224\mathrm{.}021kJ$ and $S=-0\mathrm{.}1714k\frac{J}{K}.$ Take as a basis $1$mol of $H_2$ burned to form the flue gases and $T_{}=300K.$

Make a thermodynamic analysis of the process. Represent your results in a table including $W_{\text{n}\text{e}\text{t}\text{,}}{W}_{\text{i}\text{d}\text{e}\text{a}\text{l}}$ and $W_{\text{l}\text{o}\text{s}\text{t}\text{.}\text{C}\text{a}\text{l}\text{c}\text{u}\text{l}\text{a}\text{t}\text{e}\text{a}\text{l}\text{l}\text{w}\text{o}\text{r}\text{k}\text{v}\text{a}\text{l}\text{u}\text{e}\text{s}as}$ as percentage of $W_{\text{i}\text{d}\text{e}\text{a}\text{l}}.$ Evaluate the thermodynamic efficiency $({}_t)$ of the process.

PS: There is no heat transfer between surroundings and the boiler.

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