--- title: "Gas turbine 6:1: power output and efficiency" subject: "Power Plant Equipment" chapter: 6 key: "semester_7/power_plant_equipment:gt-6-1-power-efficiency" source: https://www.bctengineer.com/q/semester_7/power_plant_equipment/gt-6-1-power-efficiency site: BCT Engineering --- # Gas turbine 6:1: power output and efficiency Power Plant Equipment · Chapter 6: Gas Turbine Power Plant - Asked in: 2079 Bhadra, 8 marks - Video: [Calculation of various parameters for an Open Cycle Gas Turbine Power Plant | Prof. D. P. Kamble](https://www.youtube.com/watch?v=yOK7mg-OjCQ) — Mech Engg - 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-efficiency - 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 80% and 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. Find the thermal efficiency of the plant as well. Take Cp = 1.005 kJ/kg K and γ = 1.4 for the compression process, Cp = 1.11 kJ/kg K and γ = 1.333 for the expansion process and Cp = 1.11 kJ/kg K for the combustion process. ## Short answer Compressor work = 241.87 kJ/kg, turbine work = 290.01 kJ/kg, net work 48.14 kJ/kg. Power output = 16 kg/s × 48.14 = 770.3 kW. Thermal efficiency = 12.24%. ## 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: $c_p = 1.005$, $\gamma = 1.4$ ($\frac{\gamma-1}{\gamma} = 0.2857$). Expansion: $c_p = 1.11$, $\gamma = 1.333$ ($\frac{\gamma-1}{\gamma} = 0.2498$). Combustion: $c_p = 1.11$ kJ/kg K. Mass of fuel neglected. ```text 1 2 3 4 --> [C] ---> [CC] ---> [T] ---> exhaust \================/ ==> Generator ``` #### Compressor $$ \begin{aligned} T_{2s} &= 288 \times 6^{0.2857} = 480.53\ \text{K} \\ T_2 &= 288 + \frac{480.53 - 288}{0.80} = 528.66\ \text{K} \\ W_c &= 1.005(528.66 - 288) = 241.87\ \text{kJ/kg} \end{aligned} $$ #### Turbine $$ \begin{aligned} T_{4s} &= \frac{883}{6^{0.2498}} = \frac{883}{1.5646} = 564.38\ \text{K} \\ T_4 &= 883 - 0.82(883 - 564.38) = 621.73\ \text{K} \\ W_t &= 1.11(883 - 621.73) = 290.01\ \text{kJ/kg} \end{aligned} $$ #### Power output $$ \begin{aligned} W_{net} &= 290.01 - 241.87 = 48.14\ \text{kJ/kg} \\ P &= \dot m W_{net} = 16 \times 48.14 = 770.3\ \text{kW} \end{aligned} $$ #### Thermal efficiency $$ \begin{aligned} Q_s &= c_p (T_3 - T_2) = 1.11(883 - 528.66) = 393.31\ \text{kJ/kg} \\ \eta_{th} &= \frac{48.14}{393.31} = 0.1224 = 12.24\% \end{aligned} $$ **Answer:** Generator power output ≈ **770.3 kW** (assuming no mechanical/generator losses); thermal efficiency = **12.24 %**. ## Check yourself The answer's key points as multiple-choice questions, with the correct option and why. 1. Which cp and gamma are used for compression and expansion? A. 1.11 for both B. 1.005 for both C. 1.4 for expansion D. 1.005 and 1.4 for compression; 1.11 and 1.333 for expansion Answer: D. Hot gas has different properties from air. (Key point: Different gas properties) 2. Net work per kg is A. Wt - Wc = 290.01 - 241.87 = 48.14 kJ/kg B. Wt + Wc C. Wc - Wt D. Wt only Answer: A. Generator power = 16 x 48.14 = 770.3 kW. (Key point: Net work) 3. Actual T4 is A. T4s = 564 K B. T3 - 0.82(T3 - T4s) = 621.7 K C. T3 - (T3 - T4s)/0.82 D. 883/6 Answer: B. Efficiency scales the isentropic drop. (Key point: Turbine exit) 4. Thermal efficiency is A. Wnet / cp(T3 - T4) B. Wt / Wc C. Wnet / cp(T3 - T2) = 12.24% D. Wnet / Wt Answer: C. Heat supplied is 393.3 kJ/kg. (Key point: Thermal efficiency) ## Close variants set in other exams - [Gas turbine 6:1: generator power output](https://www.bctengineer.com/question.md?key=semester_7%2Fpower_plant_equipment%3Agt-6-1-power-output) — Power Plant Equipment, chapter 6, asked 2× ## Related in Power Plant Equipment - [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 - [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× - [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 - [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 - [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