GATE AE 2017 • Q48 NAT • 2 Marks Propulsion

Propulsion

Compressors and Turbines

Subtopic: Axial Flow Gas Turbines & Blade Cooling

Question Statement:

Air, at 450 K stagnation temperature and at a rate of 50 kg/s, enters an axial turbine stage and leaves at 350 K stagnation temperature. Taking specific heat at constant pressure $C_p = 1005$ J/(kg K), the power output (in MW) from the turbine is _________ (round off to 2 decimal places).

Official Answer Key:

5.03

Step-by-Step Solution & Explanation

### **Detailed Step-by-Step Solution (GATE AE 2017 Q.48)** **1. Intuitive Physical Setup & Given Parameters**: - Mass flow rate of air: $\dot{m} = 50\text{ kg/s}$ - Inlet total temperature: $T_{01} = 450\text{ K}$ - Exit total temperature: $T_{02} = 350\text{ K}$ - Specific heat of air: $C_p = 1005\text{ J/(kg K)}$ **2. Step-by-Step Mathematical Derivation**: 1. **Steady Flow Energy Equation (SFEE) across Adiabatic Turbine**: P_{output} = \dot{m} \Delta h_0 = \dot{m} C_p (T_{01} - T_{02}) 2. **Total Temperature Drop**: \Delta T_0 = 450 - 350 = 100\text{ K} 3. **Evaluating Power Output**: P_{output} = 50\text{ kg/s} \times 1005\text{ J/(kg K)} \times 100\text{ K} = 5025000\text{ W} = 5.025\text{ MW} Rounding to two decimal places: P_{output} \approx 5.03\text{ MW} Official acceptable range: **[5.00, 5.05] MW**. **3. Comprehensive Options & Distractor Analysis**: - **Question Type**: Numerical Answer Type (NAT). - **Official Range**: **5.00 to 5.05 MW**. **4. Official Master Key & Exam Takeaway**: - **Official Answer**: **5.03** - **Key Formula**: $P = \dot{m} C_p \Delta T_0$.
← Previous (Q47) All 2017 Questions Next (Q49) →

Related Compressors and Turbines Solved Questions

View All Compressors and Turbines PYQs →
GATE AE 2026 Q18 MCQ • 1M

The figure below depicts two ideal gas turbine cycles, cycle 1-2-3-4-1 and cycle 1-2-3'-4'-1, on a T-s diagram. Which one the following statements is FALSE?
GATE AE 2026 Q27 MSQ • 1M

The figure below shows the blading of the rotors of two different axial turbomachines under their typical operating conditions, labelled as Configuration I and Configuration II. Which of the following statements is/are TRUE?
GATE AE 2026 Q28 MSQ • 1M

A multi-stage axial compressor can be operated at two points, A and B, both of which lie on the same speed line, as shown in the figure below. If $\eta$ is the isentropic efficiency of the compressor, select the statements that is/are TRUE.
GATE AE 2026 Q42 MCQ • 2M

The figure below shows a compressor stage with station numbers 1, 2, and 3 as indicated. If p0i, T0i, and Ci refer to the average values of total pressure, total temperature, and absolute flow speed, respectively, at the ith station, select the CORRECT option considering losses.

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