Problem $1$

A gas turbine $($Brayton$)$ cycle is used as the topping cycle for a steam power plant as shown in the diagram. The states are given in the table. $\backslash$begin$\{$tabular$\}\{$lllllr$\}$

& $\backslash (\backslash$mathrm$\{$T$\}[\backslash$mathrm$\{$i$\}]\backslash )$ & $\backslash (\backslash$mathrm$\{$p$\}[\backslash$mathrm$\{$i$\}]\backslash )$ & $\backslash (\backslash$mathrm$\{$h$\}[\backslash$mathrm$\{$i$\}]\backslash )$ & $\backslash (\backslash$mathrm$\{$s$\}[\backslash$mathrm$\{$i$\}]\backslash )$ & $\backslash (\backslash$mathrm$\{$h$\}\_\{-\}\backslash$mathrm$\{$s$\}[\backslash$mathrm$\{$i$\}]\backslash )\backslash \backslash$

State & K & bar & $\{\backslash ([\backslash$mathrm$\{$kJ$\}/\backslash$mathrm$\{$kg$\}]\backslash )\}$ & $\{\backslash ([\backslash$mathrm$\{$kJ$\}/\backslash$mathrm$\{$kg$\}-\backslash$mathrm$\{$K$\}]\backslash )\}$ & $\{\backslash ([\backslash$mathrm$\{$kJ$\}/\backslash$mathrm$\{$kg$\}]\backslash )\}\backslash \backslash$

& & & & & $\backslash \backslash$

$\backslash$hline $1$ & $300$ & $1\mathrm{.}0$ & $300\mathrm{.}4$ & $5\mathrm{.}702$ & $-\backslash \backslash$

$\backslash$hline $2$ & $655\mathrm{.}6$ & $12\mathrm{.}0$ & $665\mathrm{.}8$ & $5\mathrm{.}789$ & $611\backslash \backslash$

$\backslash$hline $3$ & $1500$ & $12\mathrm{.}0$ & $1635\mathrm{.}4$ & $6\mathrm{.}731$ & $-\backslash \backslash$

$\backslash$hline $4$ & $900\mathrm{.}3$ & $1\mathrm{.}1$ & $933\mathrm{.}3$ & $6\mathrm{.}821$ & $855\mathrm{.}3\backslash \backslash$

$\backslash$hline $5$ & $494\mathrm{.}9$ & $1\mathrm{.}0$ & $497\mathrm{.}9$ & $6\mathrm{.}208$ & $-\backslash \backslash$

$\backslash$hline $6$ & $850$ & $8\mathrm{.}0$ & $3644\mathrm{.}6$ & $8\mathrm{.}069$ & $-\backslash \backslash$

$\backslash$hline $7$ & $646\mathrm{.}1$ & $2\mathrm{.}0$ & $3219\mathrm{.}4$ & $8\mathrm{.}135$ & $3177\backslash \backslash$

$\backslash$hline $8$ & $311\mathrm{.}7$ & $0\mathrm{.}1$ & $2572\mathrm{.}3$ & $8\mathrm{.}346$ & $2508\backslash \backslash$

$\backslash$hline $9$ & $309\mathrm{.}4$ & $0\mathrm{.}1$ & $151\mathrm{.}5$ & $0\mathrm{.}521$ & $-\backslash \backslash$

$\backslash$hline $10$ & $309\mathrm{.}4$ & $2\mathrm{.}0$ & $151\mathrm{.}8$ & $0\mathrm{.}521$ & $151\mathrm{.}7\backslash \backslash$

$\backslash$hline $11$ & $393\mathrm{.}4$ & $2\mathrm{.}0$ & $504\mathrm{.}5$ & $1\mathrm{.}530$ & $-\backslash \backslash$

$\backslash$hline $12$ & $393\mathrm{.}5$ & $8\mathrm{.}0$ & $505\mathrm{.}6$ & $1\mathrm{.}531$ & $505\mathrm{.}2\backslash \backslash$

$\backslash$hline

$\backslash$end$\{$tabular$\}$ a$)$ The isentropic efficiency of the gas turbine is$?$

$0\mathrm{.}9$

b$)$ The heat added in the combustor per kg of gas?

$\backslash (969\mathrm{.}6\backslash$mathrm$\{$~kJ$\}/\backslash$mathrm$\{$kg$\}\backslash )$

c$)$ The net work of the gas turbine cycle per kg of gas?

$\backslash [$

$336\mathrm{.}7\backslash$mathrm$\{$~kJ$\}/\backslash$mathrm$\{$kg$\}$

$\backslash ]$

d$)$ The mass of steam entering the open feed water heater at state $7$ per kg of steam leaving the heater at state $11.$

$0\mathrm{.}115$

e$)$ The net work of the steam cycle per kg of steam.

$\backslash (996\mathrm{.}5\backslash$mathrm$\{$~kJ$\}/\backslash$mathrm$\{$kg$\}\backslash )$

f$)$ The ratio of the gas flow rate to the steam flow rate.

$7\mathrm{.}21$

g$)$ The cycle efficiency $($for the two cycles operating together$).$

$0\mathrm{.}49$