Please include any and all calculations. Please also mention which tables are referenced. Thanks A$.$ A Rankine cycle with reheat and superheat is shown in Fig. A$.$ The pressure in the steam generator is $160$ bar $(\backslash ($ p$\_\{1\}=$p$\_\{6\}=160\backslash$mathrm$\{$bar$\}\backslash )),$ the intermediate pressure at the exit of the first stage of the turbine is $15$ bar $(\backslash ($ p$\_\{2\}=$p$\_\{3\}=\backslash )15$ bar $)$ and the pressure in the condenser is $\backslash (1\mathrm{.}5\backslash$mathrm$\{$bar$\}\backslash$left$($p$\_\{4\}=$p$\_\{5\}=1\mathrm{.}5\backslash$mathrm$\{$bar$\}\backslash$right$.\backslash )).$ The working fluid is water $($mass flow rate, $\backslash (\backslash$dot$\{$m$\}=2\mathrm{.}3\backslash$mathrm$\{$~kg$\}/\backslash$mathrm$\{$s$\}\backslash )).$ The turbine $($both stages$)$ and the pump operate adiabatically. At the exit of both stages of the turbine, the working fluid is saturated vapor $($points $2$ and $4).$ At the exit of the condenser $($point $5),$ the working fluid is saturated liquid. Do the following analysis:

$($a$)$ What is the state of water at point $1$ if the temperature is $\backslash ($ T$\_\{1\}=520^\{\backslash$circ$\}\backslash$mathrm$\{$C$\}\backslash )?[2]$

$($b$)$ Determine the specific enthalpy and the specific entropy of the working fluid at point $1.$

$($c$)$ Determine the isentropic coefficient of the first stage of the turbine. $[6]$

$($d$)$ If the expansion of the working fluid in the second stage of the turbine is isentropic$,$ determine the state of the working fluid at point $3,$ as well as its temperature and specific enthalpy

$($e$)$ If the isentropic coefficient of the pump is $\backslash (85\backslash \%\backslash ),$ determine the specific enthalpy of the working fluid at point $6.$

$($f$)$ Determine the state of water at point $6.$ Calculate the temperature of the working fluid at point $6.$ Verify, that the compression of the working fluid causes an increase in the entropy generation, by applying $2$ nd Law for open systems around the pump and determining the rate of entropy generation in W$/$K$.$

$($g$)$ Sketch the entropy$-$temperature diagram of this cycle

$($h$)$ Determine the power of the turbine in kW $,$ the power spent on the pump in kW $,$ and the net power output of the cycle in kW $.$

$($i$)$ Determine the rate of heat, $\backslash (\backslash$dot$\{$Q$\}\_\{$i n$\}\backslash ),$ added to the steam generator in kW and the rate of heat, $\backslash (\backslash$dot$\{$Q$\}\_\{\backslash$text $\{$out $\}\}\backslash ),$ rejected from the working fluid to the condenser cooling water in kW$.$ Verify your result for the net power output of the cycle in $($ h $).$ Determine the thermal efficiency of the cycle.

$($j$)$ Determine the mass flow rate of the condenser cooling water, in $\backslash (\backslash$mathrm$\{$kg$\}/\backslash$mathrm$\{$h$\}\backslash ),$ if cooling water enters the condenser at $\backslash (12^\{\backslash$circ$\}\backslash$mathrm$\{$C$\}\backslash )$ and exits at $\backslash (36^\{\backslash$circ$\}\backslash$mathrm$\{$C$\}\backslash ).$