In an ideal Brayton cycle for a gas turbine engine, which of the following processes correctly represents the heat addition and rejection?
Options:
(A) Heat addition at constant volume, heat rejection at constant pressure
(B) Heat addition at constant pressure, heat rejection at constant pressure
(C) Heat addition at constant volume, heat rejection at constant volume
(D) Heat addition at constant temperature, heat rejection at constant temperature
Official Answer Key:
B
Step-by-Step Solution & Explanation
### **Detailed Step-by-Step Solution (GATE AE 2018 Q.26)**
**1. Intuitive Physical Setup & Given Parameters**:
- The standard air-standard Brayton cycle models ideal gas turbine and jet engine operation.
**2. Step-by-Step Thermodynamic Derivation**:
1. **Four Ideal Processes of Brayton Cycle**:
- $1 \to 2$: Isentropic (reversible adiabatic) compression in the compressor.
- $2 \to 3$: Isobaric (constant pressure) heat addition in the combustor ($P_2 = P_3$).
- $3 \to 4$: Isentropic expansion in the turbine and nozzle.
- $4 \to 1$: Isobaric (constant pressure) heat rejection to the atmosphere ($P_4 = P_1$).
2. Both heat addition and heat rejection occur at constant pressure.
**3. Comprehensive Options & Distractor Analysis**:
- **(A)** (constant volume addition): ❌ Incorrect. That describes the Otto or Dual cycle.
- **(B)** (constant pressure addition and rejection): ✅ **CORRECT**. Defines the isobaric combustor and exhaust of the Brayton cycle.
- **(C)** (constant volume addition and rejection): ❌ Incorrect. That is the Otto cycle.
- **(D)** (isothermal addition and rejection): ❌ Incorrect. That is the Carnot or Ericsson cycle.
**4. Official Master Key & Exam Takeaway**:
- **Official Answer**: **B**
- **Exam Rule**: Brayton cycle = 2 Isentropics + 2 Isobars.
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