Gas turbine 6:1: generator power output

Data: $r_p = 6$, $T_3 = 610 + 273 = 883$ K, $\eta_c = 0.80$, $\eta_t = 0.82$, $T_1 = 15 + 273 = 288$ K, $\dot m = 16$ kg/s. Compression: $c_p = 1.005$ kJ/kg K, $\gamma = 1.4$ ($\frac{\gamma-1}{\gamma} = 0.2857$). Expansion: $c_p = 1.11$ kJ/kg K, $\gamma = 1.333$ ($\frac{\gamma-1}{\gamma} = 0.2498$). Fuel mass and mechanical losses neglected.

 1        2          3        4
 --> [C] ---> [CC] ---> [T] ---> exhaust
      \================/  ==> Generator

Compressor work

$$\begin{aligned} T_{2s} &= T_1 r_p^{0.2857} = 288 \times 1.6685 = 480.53\ \text{K} \\ T_2 &= T_1 + \frac{T_{2s} - T_1}{\eta_c} = 288 + \frac{192.53}{0.80} = 528.66\ \text{K} \\ W_c &= 1.005(528.66 - 288) = 241.87\ \text{kJ/kg} \end{aligned}$$

Turbine work

$$\begin{aligned} T_{4s} &= \frac{T_3}{r_p^{0.2498}} = \frac{883}{1.5646} = 564.38\ \text{K} \\ T_4 &= T_3 - \eta_t (T_3 - T_{4s}) = 883 - 0.82 \times 318.62 = 621.73\ \text{K} \\ W_t &= 1.11(883 - 621.73) = 290.01\ \text{kJ/kg} \end{aligned}$$

Power output

$$\begin{aligned} W_{net} &= W_t - W_c = 290.01 - 241.87 = 48.14\ \text{kJ/kg} \\ P &= \dot m W_{net} = 16 \times 48.14 = 770.3\ \text{kW} \end{aligned}$$

(Turbine power = 4640.2 kW, of which the compressor absorbs 3869.9 kW.)

Answer: Power output of the generator ≈ 770 kW.