A single shaft gas turbine has a pressure ratio of $10/1$ and a maximum cycle temperature of $700\backslash$deg C$.$ The

isentropic efficiencies of the compressor and turbine are $0\mathrm{.}82$ and $0\mathrm{.}85$ respectively. The air enters the

compressor at $15\backslash$deg C at the rate of $15$kg$/$s$.$ Take cP $=1\mathrm{.}005$ kJ$/$kg K and $\backslash$gamma $=1\mathrm{.}4$ for the compression process,

and take cP $=1\mathrm{.}11$ kJ$/$kg K and $\backslash$gamma $=1\mathrm{.}333$ for the expansion process. Assuming that cP for the combustion

process is $1\mathrm{.}11$ kJ$/$kg K$,$

b$)$ Calculate:

$($i$)$ the cycle efficiency

$($ii$)$ the work ratio of the plant.

c$)$ Compare and evaluate the efficiency of the above single shaft gas turbine with the theoretical

efficiency in a similar system. Account for any discrepancies found.