--- title: "Gas turbine 6:1: generator power output" subject: "Power Plant Equipment" chapter: 6 key: "semester_7/power_plant_equipment:gt-6-1-power-output" source: https://www.bctengineer.com/q/semester_7/power_plant_equipment/gt-6-1-power-output site: BCT Engineering --- # Gas turbine 6:1: generator power output Power Plant Equipment · Chapter 6: Gas Turbine Power Plant - Asked in: 2075 Chaitra, 10 marks - Video: [Example 9.1: Calculating the power output from a gas turbine unit working on Open Brayton's cycle](https://www.youtube.com/watch?v=w_smCBy-iYc) — Dr. Arshad Ali Khan Official - Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14 - Page: https://www.bctengineer.com/q/semester_7/power_plant_equipment/gt-6-1-power-output - Whole chapter: https://www.bctengineer.com/md/semester_7/power_plant_equipment/chapter-6 ## Question A gas turbine unit has a pressure ratio of 6:1 and maximum cycle temperature of 610°C. The isentropic efficiencies of the compressor and turbine are 0.80 and 0.82 respectively. Calculate the power output in kilowatts of an electric generator geared to the turbine when the air enters the compressor at 15°C at the rate of 16 kg/s. Take cp = 1.005kJ/kgK and γ = 1.4 for the compression process, and take cp=1.11kJ/kg K and γ = 1.333 for the expansion process. ## Short answer Compressor work 241.87 kJ/kg, turbine work 290.01 kJ/kg, net work 48.14 kJ/kg. Generator output = 16 kg/s × 48.14 = 770 kW. ## Answer **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. ```text 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**. ## Check yourself The answer's key points as multiple-choice questions, with the correct option and why. 1. Why are two sets of cp and gamma used in this problem? A. Compression handles cold air (1.005, 1.4) and expansion handles hot gas (1.11, 1.333) B. The question gives errors C. Compressor uses gamma 1.333 D. Fuel mass is included in the compressor Answer: A. The problem specifies air properties for compression and combustion-gas properties for expansion. (Key point: Different gas properties) 2. With T1 = 288 K, T2s = 480.53 K and eta_c = 0.80, what is the compressor work? A. 1.005 x 192.53 = 193.5 kJ/kg B. 1.005 x 240.66 = 241.87 kJ/kg C. 1.11 x 240.66 = 267.1 kJ/kg D. 1.005 x 480.53 = 482.9 kJ/kg Answer: B. Actual rise = 192.53/0.80 = 240.66 K, times cp = 1.005 gives 241.87 kJ/kg. (Key point: Compressor work) 3. For the turbine, the actual temperature drop is: A. T3 - T4s = 318.62 K B. eta_t x (T3 - T4s) = 261.27 K C. (T3 - T4s)/eta_t = 388.6 K D. T4s x eta_t = 462.8 K Answer: B. Actual drop = 0.82 x 318.62 = 261.27 K, and Wt = 1.11 x 261.27 = 290.01 kJ/kg. (Key point: Turbine work) 4. Which gives the generator power? A. 16 x 290.01 = 4640 kW B. 16 x 241.87 = 3870 kW C. 16 x (290.01 - 241.87) = 770 kW D. (290.01 - 241.87)/16 = 3 kW Answer: C. Net specific work 48.14 kJ/kg times 16 kg/s is about 770 kW; most of the 4640 kW turbine power is absorbed by the compressor. (Key point: Power output) ## Close variants set in other exams - [Gas turbine 6:1: power output and efficiency](https://www.bctengineer.com/question.md?key=semester_7%2Fpower_plant_equipment%3Agt-6-1-power-efficiency) — Power Plant Equipment, chapter 6, asked 2× ## Related in Power Plant Equipment - [Two-shaft gas turbine, pressure ratio 7:1](https://www.bctengineer.com/question.md?key=semester_7%2Fpower_plant_equipment%3Agt-two-shaft-7-1) — Power Plant Equipment, chapter 6, asked 2× - [Gas turbine 5:1: power, efficiency, work ratio](https://www.bctengineer.com/question.md?key=semester_7%2Fpower_plant_equipment%3Agt-5-1-work-ratio) — Power Plant Equipment, chapter 6 - [Open cycle gas turbine on heavy oil](https://www.bctengineer.com/question.md?key=semester_7%2Fpower_plant_equipment%3Agt-heavy-oil-capacity) — Power Plant Equipment, chapter 6 - [Gas turbine 800 kW with regenerator](https://www.bctengineer.com/question.md?key=semester_7%2Fpower_plant_equipment%3Agt-800kw-regenerator) — Power Plant Equipment, chapter 6, asked 2× - [Regenerative gas turbine: 1 to 6.9 bar](https://www.bctengineer.com/question.md?key=semester_7%2Fpower_plant_equipment%3Agt-regenerative-6-9-bar) — Power Plant Equipment, chapter 6 - [Gas turbine with 78% effective regenerator](https://www.bctengineer.com/question.md?key=semester_7%2Fpower_plant_equipment%3Agt-regenerator-78) — Power Plant Equipment, chapter 6 ## Related in other subjects - [Ideal gas turbine 100 kW: pressure ratio, work, efficiency](https://www.bctengineer.com/question.md?key=semester_2%2Ffundamental_of_thermodynamics_and_heat_transfer%3Aideal-gas-turbine-100kw-pressure-ratio) — Fundamental of Thermodynamics & Heat Transfer, chapter 6 - [Actual gas turbine cycle with component efficiencies](https://www.bctengineer.com/question.md?key=semester_7%2Fturbo_machines%3Aactual-brayton-cycle-numerical) — Turbo Machines, chapter 3 - [Brayton cycle 80 MW: mass flow, efficiency, compressor fraction](https://www.bctengineer.com/question.md?key=semester_2%2Ffundamental_of_thermodynamics_and_heat_transfer%3Abrayton-80mw-300k-1500k-fraction) — Fundamental of Thermodynamics & Heat Transfer, chapter 6 - [Gas turbine power from isentropic efficiency](https://www.bctengineer.com/question.md?key=semester_7%2Fturbo_machines%3Agas-turbine-power-isentropic-efficiency) — Turbo Machines, chapter 1