Mechanical Engineering 2024 Paper II 50 marks Solve

Q8

(a) A cogenerating steam power plant operates with a boiler output of 25 kg/s steam at 7 MPa, 500°C. The condenser operates at 7·5 kPa and the process heat is extracted at 5 kg/s from the turbine at 500 kPa and after use is returned as saturated liquid at 100 kPa. Assuming all components are ideal, find : (i) temperature of water leaving the condenser pump (ii) total turbine output (iii) total process heat transfer At inlet to the turbine, assume h = 3410 kJ/kg and s = 6·802 kJ/kg K Also, use data from Steam Tables given at the end. (20 marks) (b) The fuel of an IC engine contains 85% carbon, 10% hydrogen, 3% oxygen and the remaining is nitrogen in composition by weight. Determine the chemically correct Air/Fuel ratio. If 30% excess air is supplied, find the percentage composition of dry products of combustion exhaust by weight and by volume. (20 marks) (c) Explain in brief, how the molecular structure of the IC engine fuels affects the tendency to knock. (10 marks)

हिंदी में प्रश्न पढ़ें

(a) एक सह-उत्पादक भाप शक्ति संयंत्र बॉयलर उत्पादन 25 kg/s भाप 7 MPa, 500°C पर देते हुए कार्यरत है। संघनित्र 7·5 kPa पर कार्यरत है तथा प्रक्रम की ऊष्मा 500 kPa पर, 5 kg/s की दर से टरबाइन से निकाली जाती है तथा प्रयोग के बाद 100 kPa पर संतृप्त द्रव के रूप में वापस की जाती है। सभी अवयवों को आदर्श मानते हुए, ज्ञात कीजिए : (i) संघनित्र पंप को छोड़ने वाले जल का तापमान (ii) कुल टरबाइन उत्पादन (iii) कुल प्रक्रम ऊष्मा अंतरण टरबाइन के प्रवेश पर मानिए, h = 3410 kJ/kg एवं s = 6·802 kJ/kg K अंत में संलग्न भाप सारणियों से आँकड़ों का भी प्रयोग कीजिए। (20 अंक) (b) एक अंतर्दहन (IC) इंजन के ईंधन में 85% कार्बन, 10% हाइड्रोजन, 3% ऑक्सीजन तथा शेष नाइट्रोजन, भार के अनुसार संघटन में पाया जाता है। रासायनिक रूप से सही वायु/ईंधन अनुपात का निर्धारण कीजिए। यदि 30% अतिरिक्त वायु की आपूर्ति की जाती है, तो शुष्क उत्पादों के दहन निकास का प्रतिशत संघटन, भार एवं आयतन के आधार पर ज्ञात कीजिए। (20 अंक) (c) एक अन्तर्दहन (IC) इंजन के ईंधन की आणविक संरचना उसकी अपरफोटन प्रवृत्ति को कैसे प्रभावित करती है ? संक्षेप में समझाइए। (10 अंक)

Evaluate your answer to this question → See all 2024 Mechanical Engineering questions

Directive word: Solve

This question asks you to solve. The directive word signals the depth of analysis expected, the structure of your answer, and the weight of evidence you must bring.

See our UPSC directive words guide for a full breakdown of how to respond to each command word.

How this answer will be evaluated

Approach

Solve this multi-part numerical problem by allocating approximately 40% time to part (a) cogeneration cycle analysis, 35% to part (b) combustion stoichiometry with excess air, and 25% to part (c) molecular structure-knock relationship. For (a), construct the T-s diagram showing extraction and mixing points; for (b), set up the combustion equation with 30% excess air; for (c), structure as brief comparative explanation with specific fuel examples.

Key points expected

  • Part (a)(i): Condenser pump outlet temperature = saturation temperature at 7.5 kPa ≈ 40.3°C (from steam tables)
  • Part (a)(ii): Total turbine output = ṁ_total×(h₁-h₂) + (ṁ_total-ṁ_extract)×(h₂-h₃) with proper extraction state determination at 500 kPa
  • Part (a)(iii): Process heat transfer = ṁ_extract×(h_extract - h_return) where h_return is saturated liquid enthalpy at 100 kPa
  • Part (b): Theoretical A/F = 14.57 kg air/kg fuel; with 30% excess air, actual A/F = 18.94 kg air/kg fuel
  • Part (b): Dry products composition by weight: CO₂ ≈ 18.5%, N₂ ≈ 72.3%, O₂ ≈ 9.2%; by volume: CO₂ ≈ 12.1%, N₂ ≈ 75.4%, O₂ ≈ 12.5%
  • Part (c): Straight-chain paraffins (n-heptane) knock more than branched iso-paraffins (iso-octane); aromatic rings and alcohols resist knock due to stable molecular structure
  • Part (c): Octane rating scale reference (0-100) linking molecular structure to anti-knock quality; mention of Indian fuel standards (BS-VI)

Evaluation rubric

DimensionWeightMax marksExcellentAveragePoor
Concept correctness20%10Correctly applies cogeneration cycle principles for part (a) including extraction pressure matching and mixing; for (b) uses correct atomic balances and excess air definition; for (c) accurately links carbon chain structure, branching, and bond types to knock tendency with specific fuel examples.Uses correct basic formulas but confuses extraction flow rates in (a) or miscalculates excess air factor in (b); for (c) gives generic knock explanation without structural specificity.Treats cogeneration as simple Rankine cycle ignoring extraction; uses volume basis instead of mass basis for combustion calculations; describes knock as only compression-ratio dependent ignoring fuel chemistry.
Numerical accuracy25%12.5All numerical values accurate: (a)(i) T ≈ 40.3°C, (a)(ii) turbine output ≈ 22.5-23 MW range with correct enthalpy interpolations, (a)(iii) process heat ≈ 4.5-5 MW; (b) theoretical A/F = 14.57, actual = 18.94, dry product percentages within ±0.5% of correct values; proper significant figures and unit handling throughout.Correct methodology but minor steam table interpolation errors or rounding in (a); A/F ratio correct but product composition off by 1-2% due to arithmetic; units mostly consistent.Order-of-magnitude errors in turbine power (confusing kW and MW); incorrect excess air application (adds 30% to products instead of to air); no units or inconsistent units (kJ/kg vs MJ/kg).
Diagram quality15%7.5Clear T-s diagram for part (a) showing: boiler outlet (7 MPa, 500°C), expansion line with extraction point at 500 kPa, condenser at 7.5 kPa, feed pump, and process heat return at 100 kPa; all state points numbered and matched to calculations; for (c) may include molecular structure sketches of n-heptane vs iso-octane.T-s diagram drawn but extraction point not clearly marked or process heat loop omitted; states labelled but not clearly linked to numerical values.No diagram provided; or h-s diagram used incorrectly; or schematic flow diagram without thermodynamic states shown.
Step-by-step derivation25%12.5Explicit stepwise working: (a) mass balance at extraction, entropy equality for isentropic expansion with steam table lookups, energy balances for each turbine section and process heater; (b) complete combustion equation setup, atomic balances for C-H-O-N, theoretical air calculation, excess air application, then product mole-to-mass conversion; (c) logical progression from molecular structure to flame speed to knock tendency.Key equations shown but skips intermediate steps like entropy interpolation or jumps from moles to mass without showing conversion; combustion equation correct but balancing shown partially.Final answers stated without derivation; or incorrect formula application (e.g., using isentropic relations for ideal gas for steam); no working visible for steam table interpolations.
Practical interpretation15%7.5For (a), comments on utilization factor or energy efficiency advantage of cogeneration over separate heat and power; for (b), relates excess air to practical boiler operation and emission implications (NOx formation); for (c), connects to Indian automotive fuels (octane ratings of petrol, cetane for diesel) and relevance to engine design for BS-VI compliance.Brief mention of cogeneration benefit or knock rating relevance but not developed; no connection to Indian standards or practical engine operation.No interpretation provided; treats all parts as purely academic exercises without engineering context.

Practice this exact question

Write your answer, then get a detailed evaluation from our AI trained on UPSC's answer-writing standards. Free first evaluation — no signup needed to start.

Evaluate my answer →

More from Mechanical Engineering 2024 Paper II