A gas turbine operates between an inlet pressure of 15 bar and an exhaust pressure of 1.2 bar. The inlet temperature to the turbine is \(1500 \mathrm{~K}\) and the turbine has an isentropic efficiency of \(90 \%\). The surroundings are at a pressure of 1 bar and a temperature of \(300 \mathrm{~K}\). Calculate, for the turbine alone:

(i) The specific power output;

(ii) The exhaust gas temperature;

(iii) The exergy change in the gas passing through the turbine and

(iv) The irreversibility or lost work.

Assume the working substance is an ideal gas with a specific heat at constant pressure of \(c_{p}=1.005 \mathrm{~kJ} / \mathrm{kg} \mathrm{K}\) and the specific gas constant, \(R=0.287 \mathrm{~kJ} / \mathrm{kg} \mathrm{K}\).

[697.5 kJ/kg; \(806 \mathrm{~K} ; 727.7 \mathrm{~kJ} / \mathrm{kg} ; 343.6 \mathrm{~kJ} / \mathrm{kg}\) ]