--- title: "Brayton cycle working principle with P-v and T-s" subject: "Fundamental of Thermodynamics & Heat Transfer" chapter: 6 key: "semester_2/fundamental_of_thermodynamics_and_heat_transfer:brayton-cycle-working-principle" source: https://www.bctengineer.com/q/semester_2/fundamental_of_thermodynamics_and_heat_transfer/brayton-cycle-working-principle site: BCT Engineering --- # Brayton cycle working principle with P-v and T-s Fundamental of Thermodynamics & Heat Transfer · Chapter 6: Thermodynamic Cycles - Asked in: 2074 Bhadra, 6 marks - Video: [Brayton Cycle](https://www.youtube.com/watch?v=17-2uYI76k4) — TutorialsPoint - Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14 - Page: https://www.bctengineer.com/q/semester_2/fundamental_of_thermodynamics_and_heat_transfer/brayton-cycle-working-principle - Whole chapter: https://www.bctengineer.com/md/semester_2/fundamental_of_thermodynamics_and_heat_transfer/chapter-6 ## Question Explain the working principle of Brayton cycle with corresponding processes on P-v and T-s diagrams. ## Short answer The Brayton cycle consists of isentropic compression, constant-pressure heat addition, isentropic expansion, and constant-pressure heat rejection. Air is compressed, heated in a combustor, expanded through a turbine, and exhausted. Net work output equals turbine work minus compressor work. ## Answer The Brayton cycle is the ideal air-standard cycle for gas turbines and jet engines. Air, the working fluid, is compressed, heated at constant pressure and expanded in a turbine. The turbine produces more work than the compressor takes, and the difference is the net output. ```text Fuel (Q_in) | v 2 +-------------+ 3 +----->| Combustor |------+ | +-------------+ | | v [Compressor]=======shaft=======[Turbine]---> net work ^ | | 1 4 v Air in Exhaust ``` #### Processes 1. **1-2: Isentropic compression** in the compressor. Pressure and temperature rise; work is supplied. 2. **2-3: Constant-pressure heat addition** in the combustor (a heat exchanger in the ideal cycle). The temperature rises to the maximum, T₃. 3. **3-4: Isentropic expansion** in the turbine. Work is produced; part of it drives the compressor. 4. **4-1: Constant-pressure heat rejection** to the atmosphere (the hot exhaust cools to the inlet state). ```text P-v diagram T-s diagram P T | 2 ____________ 3 | 3 | \ \ | /| | \ \ | / | | '. '. | / | | '. '. | 2 _.-' | | '-._ '-._ | | 4 | '- 1 _________ 4 | | .-' | | | _.-' | | 1.-' +----------------------> v +--------------------> s 1-2 isentropic compression 2-3 constant-P heat addition 3-4 isentropic expansion 4-1 constant-P heat rejection ``` #### Key results - q_in = cp (T₃ − T₂), q_out = cp (T₄ − T₁) - w_net = q_in − q_out - η = 1 − 1/r_p^((γ−1)/γ), where r_p = P₂/P₁ A high pressure ratio gives high efficiency. The back-work ratio (compressor work/turbine work) is large, about 40-80 % for gas turbines. ## Check yourself The answer's key points as multiple-choice questions, with the correct option and why. 1. Why does the Brayton cycle give net work? A. Heat rejection is zero B. Compressor work exceeds turbine work C. Turbine work exceeds compressor work D. Pump work is negligible Answer: C. Hot gas expands through the turbine giving more work than the compressor uses. (Key point: Net output) 2. Process 2-3 is: A. Constant-pressure heat addition B. Isothermal compression C. Isentropic expansion D. Constant-volume heat addition Answer: A. Fuel is burned in the combustor at constant pressure, raising T to T3. (Key point: Heat addition) 3. Process 4-1 is: A. Throttling B. Constant-pressure heat rejection to atmosphere C. Constant-volume rejection D. Isentropic compression Answer: B. Exhaust cools at constant pressure to the inlet state. (Key point: Process 4-1) 4. Efficiency of the ideal Brayton cycle rises with: A. Higher pressure ratio B. Lower pressure ratio C. Lower gamma only D. Larger air flow Answer: A. eta = 1 - 1/r_p^((g-1)/g). 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