Problem $3$: A steam power plant, operating on a non$-$ideal Rankine cycle, is used to generate power. The power output by the cycle is used to drive an air compressor, as shown in the diagram. The steam$/$water flow rate in the Rankine cycle is $2\mathrm{.}5k\frac{g}{s}.$ The temperature of the surroundings may be assumed to be $25C.$ For air use: $c_{p,\text{a}\text{i}\text{r}}=1\mathrm{.}01kJk{g}^{-1}{K}^{-1}$ and $k=1\mathrm{.}4.$ Determine:

a$)$ The power input to the pump $(kW).-11\mathrm{.}71kw$

b$)$ The power output by the turbine $($kW$).2283\mathrm{.}82$ kw

c$)$ The rate at which heat is absorbed from the hot reservoir $(kW)\mathrm{.}7406\mathrm{.}13kw$

d$)$ The rate at which heat is rejected to the cold reservoir $(kW).-5134\mathrm{.}0kw$

e$)$ The thermal efficiency of the Rankine cycle. $30\mathrm{.}70,$

f$)$ The change in entropy of the hot reservoir $(k\frac{W}{K}).-11\mathrm{.}00k\frac{}{k}$

g$)$ The change in entropy of the cold reservoir $(k\frac{W}{K})17\mathrm{.}22k\frac{w}{H}$

h$)$ The entropy generation rate for the Rankine cycle $($kW$/$K$).6\mathrm{.}22k\frac{w}{K}$

i$)$ The second law efficiency of the Rankine cycle. $4$ I.

j$)$ The temperature of the air leaving the compressor if it were operated isentropically $($K$)\mathrm{.}443\mathrm{.}05$ K

k$)$ The mass flow rate of air through the compressor $(k\frac{g}{s}).11\mathrm{.}64$ kg

The actual temperature of the air leaving the compressor $(K)491\mathrm{.}42K$

$m$ The entropy generation rate for the compressor $(k\frac{W}{K}.1\mathrm{.}242k\frac{w}{k}$

n$)$ The rate at which work is lost for the entire system $(kW)\mathrm{.}2224\mathrm{.}80kw.$

The answers are given in Red, please solve on a peace of paper.

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