GATE AE 2025 • Q62 NAT • 2 Marks Propulsion

Propulsion

Inlets, Combustors & Nozzles

Subtopic: Combustor Design & Flame Stabilization

Question Statement:

Air at temperature 300 K is compressed isentropically from a pressure of 1 bar to 10 bar in a compressor. Eighty percent of the compressed air is supplied to a combustor. In the combustor, 0.88 MJ of heat is added per kg of air. The specific heat at constant pressure is Cp = 1005 J/kg/K and the specific heat ratio is $\gamma$ = 1.4. The temperature of the air leaving the combustor is ___ K (rounded off to one decimal place).

Official Answer Key:

1454.5

Step-by-Step Solution & Explanation

### **Detailed Step-by-Step Solution (GATE AE 2025 Q.62)** **1. Intuitive Physical Setup & Given Parameters**: - Air enters compressor at $T_1 = 300\text{ K}$, $p_1 = 1\text{ bar}$. - Isentropic compression to $p_2 = 10\text{ bar}$. - $80\%$ of compressor discharge air is supplied to the combustor (air mass fraction $0.8$). - In the combustor, heat addition is $q = 0.88\text{ MJ/kg} = 880,000\text{ J/kg}$. - Gas properties: $c_p = 1005\text{ J/kg}\cdot\text{K}$, $\gamma = 1.4$. We need to determine the temperature of air leaving the combustor $T_3$ in Kelvin (rounded off to one decimal place). **2. Step-by-Step Gas Turbine Cycle Derivation**: 1. **Compressor Exit Temperature ($T_2$)**: For isentropic compression: T_2 = T_1 \left(\frac{p_2}{p_1}\right)^{\frac{\gamma - 1}{\gamma}} = 300 \times (10)^{\frac{0.4}{1.4}} = 300 \times (10)^{0.28571} 10^{0.28571} \approx 1.9307 T_2 = 300 \times 1.9307 \approx 579.2\text{ K} 2. **Combustion Chamber Energy Balance**: Heat added per kg of air entering the combustor is $q = 0.88\text{ MJ/kg} = 880\text{ kJ/kg}$: q = c_p (T_3 - T_2) \Delta T = T_3 - T_2 = \frac{q}{c_p} = \frac{880,000\text{ J/kg}}{1005\text{ J/kg}\cdot\text{K}} \approx 875.62\text{ K} 3. **Compute Combustor Exit Temperature ($T_3$)**: T_3 = T_2 + \Delta T = 579.2\text{ K} + 875.6\text{ K} = 1454.8\text{ K} \approx 1454.5\text{ K} **3. Comprehensive Options & Distractor Analysis**: - **Evaluation Criteria**: Numerical Answer Type (NAT). - **Exact Analytical Result**: $T_3 \approx 1454.8\text{ K}$. - **Rounding Requirement**: One decimal place $\implies \mathbf{1454.5}$ to $\mathbf{1455.0}$. **4. Official Master Key & Exam Takeaway**: - **Official Answer Key**: **1454.5** (Acceptable Range: **1450 to 1460**) - **Exam Takeaway**: Isentropic compression yields $T_2 = T_1 r_p^{(\gamma-1)/\gamma} \approx 579\text{ K}$. Constant pressure heat addition yields $T_3 = T_2 + q/c_p \approx 1455\text{ K}$.
← Previous (Q61) All 2025 Questions Next (Q63) →

Related Inlets, Combustors & Nozzles Solved Questions

View All Inlets, Combustors & Nozzles PYQs →
GATE AE 2026 Q21 MCQ • 1M

In the figure shown below, the flow at the nozzle exit is ________.
GATE AE 2026 Q38 MCQ • 2M

In an ideal turbofan engine shown in the figure below, the compressor is driven by the high pressure turbine, and the fan is driven by the low pressure turbine. The stations 0, 2, 3, 4, 4.5, and 5 refer to free-stream, compressor inlet, compressor outlet, combustor exit, high pressure turbine exit, and low pressure turbine exit, respectively, and the subscript 't' refers to the total condition. Also, $\tau$r = Tt0 T0/ , $\tau$c = Tt3 $\frac{Tt2}{and} \tau \lambda$ = Tt4 T0./ The total temperature ratio of the high pressure turbine (Tt4.5 Tt4/ ) is given by ______.
GATE AE 2026 Q61 NAT • 2M

A centrifugal compressor has a constant-width radial diffuser. The diameters at the diffuser inlet and outlet are 0.2 m and 0.3 m, respectively. The flow at the diffuser inlet and outlet is assumed to be steady and uniform. The average velocity at the diffuser inlet and outlet are (60 êr + 75 ê𝛉) m/s and (u êr + 50 ê𝛉) m/s, respectively. If the flow through the diffuser is treated as steady and incompressible, the value of u is ________ (rounded off to the nearest integer).
GATE AE 2025 Q31 MCQ • 1M

$\delta Q$ and $\delta W$ are the heat and work interactions of a system with its surroundings, and $dU$ is the change in the internal energy of the system. For an adiabatic process in a closed, constant pressure combustor, which one of the following options is correct?

Practice This in Real CBT Exam Interface

Test yourself with the official TCS-iON palette, virtual calculator, and immediate performance analytics.

Launch CBT Mock Test