Problem HW$4\mathrm{.}5$

Solve by hand

$($or EES, your choice$)$

Water steadily circulates through the four components of a vapor power plant. The water flows through the boiler and condenser at constant pressure and through the turbine and pump adiabatically. Kinetic and potential energy effects can be ignored.

Process data follow:

Process $4-1$: constant pressure at $1$ MPa from sat. liquid to sat. vapor Process $2-3$: constant pressure at $20$ kPa from $\backslash ($ x $2=88\backslash \%\backslash )$ to $\backslash ($ x $3=18\backslash \%\backslash )$

a$)$ Using Eq$.5\mathrm{.}13$ expressed on a time$-$rate basis, determine if the cycle is internally reversible, irreversible, or impossible. Tip:

Combine the energy balances for the boiler and condenser with eq$.5\mathrm{.}13(\backslash (\backslash$sigma $\backslash )\_$dot $/$ m$\_$dot $=\backslash (0\mathrm{.}51\backslash$mathrm$\{$~kJ$\}/(\backslash$mathrm$\{$kg$\}\backslash )$ K$))$

b$)$ Determine the thermal efficiency using Eq$\mathrm{.}5\mathrm{.}4$ expressed on a time$-$rate basis and steam table data. $(18\backslash \%)$

c$)$ Compare the result of part $($b$)$ with the Carnot efficiency calculated using Eq$.5\mathrm{.}9$ with the boiler and condenser temperatures and comment. $(26\mathrm{.}5\backslash \%)$