A combined gas$-$steam powerplant uses a simple Brayton cycle for

the topping cycle and a reheat Rankine cycle for the bottoming cycle.

The $T-$s diagrams of both cycles have been calculated assuming

isentropic processes in the plant and are shown in Figure Q$2.$ The

main heat exchanger provides heat transfer between gas exhaust

$(10-11)$ and the steam $(2-3).$ A subsidiary small boiler reheats the

steam $(4-5)$ before the entry to the low pressure turbine. The

following numerical values have been obtained, $h-$ enthalpy, $s-$

entropy, $p_r-$ relative pressure. $($Note that not all these values are

required to answer the question$)$:

$h_1=191\mathrm{.}81k\frac{J}{k}g$;$s_1=0\mathrm{.}6492k\frac{J}{kgK}$;$T_1=318\mathrm{.}8K$;

$h_2=206\mathrm{.}95k\frac{J}{k}g$;$s_2=0\mathrm{.}6492k\frac{J}{kgK}$;

$h_3=3157\mathrm{.}9k\frac{J}{k}g$;$s_3=6\mathrm{.}1428k\frac{J}{kgK}$;$T_3=723K$;

$h_{4s}=2781\mathrm{.}7k\frac{J}{k}g$;$S_{4s}=6\mathrm{.}1428k\frac{J}{kgK}$;

$h_5=3457\mathrm{.}2k\frac{J}{k}g$;$s_5=7\mathrm{.}2359k\frac{J}{kgK}$;$T_5=773K$;

$h_{6s}=2292\mathrm{.}8k\frac{J}{k}g$;$s_{6s}=7\mathrm{.}2359k\frac{J}{kgK}$;$T_{6s}=318\mathrm{.}8K$;

$h_7=290\mathrm{.}16k\frac{J}{k}g$;$p_{r7}=1\mathrm{.}2311$;$T_7=290K$;

$h_{8s}=526\mathrm{.}12k\frac{J}{k}g$;$p_{r8}=9\mathrm{.}849$;$T_{8s}=522\mathrm{.}4K$;

$h_9=1515\mathrm{.}27k\frac{J}{k}g$;$p_{r9}=450\mathrm{.}5$;$T_9=1400K$

$h_{10s}=850\mathrm{.}35k\frac{J}{k}g$;$p_{r10s}=56\mathrm{.}3$;$T_{10s}=825\mathrm{.}8K$;

$h_{11}=523\mathrm{.}63k\frac{J}{k}g$;$T_{11}=520K.$

During the test runs isentropic efficiencies of the gas turbine and the

gas compressor are measured to be equal to ${}_{G_{-}}$tur $=85\%$ and

${}_{G_{-}\text{c}\text{o}\text{m}\text{p}}=80\%$ respectively. The tests on the steam high pressure and

low pressure turbines found the isentropic efficiencies of these

turbines both to be ${}_{H{P}_{{?}_{?}}\text{t}\text{u}\text{r}}={}_{L{P}_{}}$ tur $=85\%.$ Losses in the heat exchanger

and irreversible processes in the water pump can be neglected.

At steady operation of the plant, the steam is supplied with the rate of

$30k\frac{g}{sec}.$

$($a$)$ Find the gas temperature at the exit of the compressor and

gas turbine. Find enthalpies of steam at exits of both steam

turbines. Calculate the mass flow rate of air in the gas turbine

cycle.