--- title: "Closed gas turbine cycle components; thermal efficiency" subject: "Fundamental of Thermodynamics & Heat Transfer" chapter: 6 key: "semester_2/fundamental_of_thermodynamics_and_heat_transfer:closed-gas-turbine-cycle-efficiency" source: https://www.bctengineer.com/q/semester_2/fundamental_of_thermodynamics_and_heat_transfer/closed-gas-turbine-cycle-efficiency site: BCT Engineering --- # Closed gas turbine cycle components; thermal efficiency Fundamental of Thermodynamics & Heat Transfer · Chapter 6: Thermodynamic Cycles - Asked in: 2069 Poush, 6 marks - Video: [Closed Cycle Gas Turbine Power Plant](https://www.youtube.com/watch?v=FABa5iwdfiU) — BEST MECHANICAL ENGINEERING - 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/closed-gas-turbine-cycle-efficiency - Whole chapter: https://www.bctengineer.com/md/semester_2/fundamental_of_thermodynamics_and_heat_transfer/chapter-6 ## Question Sketch major components of a Closed Gas turbine cycle. Also derive its thermal efficiency. ## Short answer Components: compressor, heater (constant pressure heat addition), turbine, cooler (constant pressure heat rejection). For ideal gas with constant cp, thermal efficiency η = 1 − T1/T2 = 1 − 1/r_p^((γ−1)/γ), where r_p is the pressure ratio. ## Answer A closed gas turbine cycle uses a gas (air, helium) that circulates in a closed loop. Heat is added and rejected through heat exchangers instead of by internal combustion and exhaust. It corresponds to the ideal Brayton cycle. #### Major components ```text Heat source (Q_in) +----[ Heater ]----+ | | 2 | | 3 [Compressor] ==shaft== [Turbine] ---> Generator | | 1 | | 4 +---[ Cooler ]-----+ Heat sink (Q_out) ``` 1. **Compressor:** raises the gas pressure (1-2, isentropic). 2. **Heater (heat exchanger):** adds heat from an external source at constant pressure (2-3). 3. **Turbine:** expands the gas and delivers work (3-4, isentropic); part of the work drives the compressor. 4. **Cooler (pre-cooler):** rejects heat to cooling water or air at constant pressure (4-1). 5. A generator or load on the shaft takes the net power. #### Thermal efficiency Per kg of working gas with constant cp: q_in = cp (T₃ − T₂), q_out = cp (T₄ − T₁) η = 1 − q_out/q_in = 1 − (T₄ − T₁)/(T₃ − T₂) With r_p = P₂/P₁ = P₃/P₄, the isentropic processes give T₂/T₁ = r_p^((γ−1)/γ) = T₃/T₄ so T₄/T₁ = T₃/T₂ and (T₄ − T₁)/(T₃ − T₂) = T₁/T₂. Therefore **η = 1 − T₁/T₂ = 1 − 1/r_p^((γ−1)/γ)** The efficiency increases with the pressure ratio. A closed cycle has the advantages of using any gas, high pressure throughout (compact machines) and a clean working fluid, and it can use any heat source (such as a nuclear reactor). ## Check yourself The answer's key points as multiple-choice questions, with the correct option and why. 1. How does a closed gas turbine cycle add and reject heat? A. Through heat exchangers (heater and cooler) while the gas circulates in a loop B. By injecting fuel into the compressor C. By throttling the gas through a valve D. By internal combustion and exhaust to the atmosphere Answer: A. The gas circulates in a closed loop; a heater adds heat and a cooler rejects heat at constant pressure. (Key point: Closed cycle heat transfer) 2. What is the role of the turbine in the closed cycle? A. Adds heat at constant pressure B. Rejects heat to the cooling water C. Raises the gas pressure isentropically D. Expands the gas to deliver work, part of which drives the compressor Answer: D. The turbine (3-4) expands the gas and delivers work; part drives the compressor and the rest goes to the generator. (Key point: Component role) 3. Which relation makes (T4 - T1)/(T3 - T2) equal to T1/T2? A. P2 = P1 B. T2/T1 = T3/T4, so T4/T1 = T3/T2 C. T2 = T4 D. T1 = T3 Answer: B. Equal pressure ratios give T2/T1 = T3/T4, hence T4/T1 = T3/T2 and the ratio reduces to T1/T2. (Key point: Key step in derivation) 4. What is the thermal efficiency of the ideal closed gas turbine cycle? A. (T3 - T2)/(T4 - T1) B. 1 - r_p^((γ-1)/γ) C. 1 - T4/T3 x r_p D. 1 - 1/r_p^((γ-1)/γ) Answer: D. η = 1 - T1/T2 = 1 - 1/r_p^((γ-1)/γ); it rises with pressure ratio. 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