(a) Show in the form of a table, how the increase in the following variables affects (increase or decrease) the ignition delay period of a compression ignition (CI) engine: (i) Self-ignition temperature, (ii) Cetane number, (iii) Compression ratio, (

Question

(a) Show in the form of a table, how the increase in the following variables affects (increase or decrease) the ignition delay period of a compression ignition (CI) engine: (i) Self-ignition temperature, (ii) Cetane number, (iii) Compression ratio, (iv) Intake pressure, (v) Intake temperature, (vi) Air-fuel ratio, (vii) Exhaust gas recirculation. (10 marks)

(b) What are the desirable characteristics of an ideal working fluid for vapour power cycle? (10 marks)

(c) What is reheat factor of a steam turbine? Derive an expression to show that the reheat factor is always greater than unity. (10 marks)

(d) Compare vapour compression and vapour absorption refrigeration systems. (10 marks)

(e) Without using psychrometric chart, calculate (i) relative humidity, (ii) humidity ratio, (iii) dew point temperature and (iv) enthalpy of moist air, when DBT is 35 °C and WBT is 23 °C. The barometer reads 755 mm of Hg. Use modified Apjohn equation (take values of pressure in bar): p_v = p'_v - (1.8p(t-t'))/2700 where, p_v = partial pressure of water vapour (w.v.) corresponding to DPT, p'_v = partial pressure of w.v. corresponding to WBT, t = DBT, t' = WBT, p = barometric pressure. Use the properties of water vapour given below: t (°C) | Vapour pressure (bar) ---|--- 10 | 0·012272, 12 | 0·014017, 14 | 0·015977, 16 | 0·018173, 18 | 0·020630, 20 | 0·023373, 22 | 0·026431, 24 | 0·029832, 32 | 0·047552, 34 | 0·053201, 36 | 0·059423. (10 marks)

UPSC Answer Check · Accepted Answer

Begin with part (a) presenting a clear table with seven variables and their effects on ignition delay, citing physical reasoning for each. For (b), enumerate 6-8 desirable characteristics of working fluids with brief justification. Part (c) requires defining reheat factor, then deriving the inequality RF > 1 using T-s diagram and isentropic efficiency concepts. Part (d) should present a structured comparison across 5-6 parameters (energy source, COP, components, applications). Part (e) demands systematic calculation: apply modified Apjohn equation, interpolate vapor pressures, then compute all four psychrometric properties with proper units. Allocate time proportionally: (e) ~25%, (a)-(d) ~18.75% each.
- Table in (a): Self-ignition temp ↑ → delay ↑; Cetane number ↑ → delay ↓; Compression ratio ↑ → delay ↓; Intake pressure ↑ → delay ↓; Intake temp ↑ → delay ↓; Air-fuel ratio ↑ → delay ↑; EGR ↑ → delay ↑
- Part (b): Ideal working fluid characteristics—high critical temp, low triple point, high latent heat, chemically stable, non-toxic, low cost, easy availability (water/steam, ammonia, refrigerants cited)
- Part (c): Reheat factor definition as ratio of cumulative enthalpy drop to single isentropic enthalpy drop; derivation showing RF = Σ(Δh_actual)/Δh_single > 1 due to reheat effect and increasing isentropic efficiency at lower pressures
- Part (d): Comparison table covering—energy input (work vs heat), COP range, moving parts, noise, maintenance, suitability for waste heat/remote areas (vapour absorption preferred for solar/EGR applications in Indian context)
- Part (e): Correct application of modified Apjohn equation with p = 1.0066 bar; interpolation for p'_v at 23°C (between 22°C and 24°C); calculation of p_v, then RH, ω, DPT by interpolation, and h = c_p*t + ω*h_g

Dimension	Weight	Max marks	Excellent	Average	Poor
Concept correctness	20%	10	Correctly identifies all physical mechanisms in (a)—explains why higher cetane number reduces delay (shorter hydrocarbon chains, easier ignition); for (c) correctly defines reheat factor and explains why turbine stages after first have higher efficiency due to lower pressure ratios; in (d) accurately distinguishes work-driven vs heat-driven cycles; in (e) correctly applies psychrometric relationships.	Correct directional effects in table (a) but weak or missing explanations; basic reheat factor definition in (c) without clear inequality proof; superficial comparison in (d); mostly correct formula application in (e) with minor conceptual slips.	Reversed relationships in table (e.g., cetane number increases delay); confuses reheat factor with actual reheat in cycle; conflates compression and absorption systems; applies wrong equation in (e) or uses psychrometric chart despite prohibition.
Numerical accuracy	20%	10	Part (e): p = 755 mm Hg = 1.0066 bar; p'_v at 23°C interpolated correctly (~0.02813 bar); p_v calculated accurately using modified Apjohn; RH ≈ 35-40%; ω ≈ 0.018-0.020 kg/kg; DPT ≈ 18-20°C by interpolation; h ≈ 65-70 kJ/kg; all intermediate steps shown with 3-4 significant figures.	Correct methodology in (e) but interpolation errors or arithmetic slips; final answers within 10% of correct values; units mostly consistent but occasional bar/kPa confusion.	Major calculation errors—wrong barometric conversion, incorrect interpolation, or algebraic mistakes in Apjohn equation; answers without units or order-of-magnitude errors; no working shown for numerical parts.
Diagram quality	20%	10	Clear T-s diagram for reheat factor derivation in (c) showing expansion line with increasing slope (diverging constant pressure lines), labelled with states and isentropes; schematic of vapour compression vs absorption systems in (d) with components identified; well-structured table format in (a) with clear headers.	Basic T-s diagram in (c) without proper labelling or missing divergence illustration; simple block diagrams in (d); readable table in (a) but cramped or missing some headers.	No diagrams where required—missing T-s diagram in (c) makes derivation incomprehensible; no system schematics in (d); illegible or poorly formatted table in (a); diagrams drawn without ruler/freehand sketches.
Step-by-step derivation	20%	10	For (c): explicit derivation starting from η_stage = (h1-h2)/(h1-h2s), showing that cumulative actual enthalpy drop exceeds single isentropic drop due to reheat effect and higher stage efficiencies at lower pressure ratios; clear algebraic manipulation leading to RF > 1; for (e): systematic stepwise calculation with each formula stated before substitution.	Derivation in (c) present but skips key steps or assumes RF > 1 without proof; some steps in (e) combined or implied rather than explicit; logical flow present but gaps exist.	No derivation in (c)—merely states RF > 1; jumps to final answers in (e) without showing Apjohn equation application or interpolation method; disorganized presentation with calculations scattered.
Practical interpretation	20%	10	For (a): links ignition delay to diesel knock and engine noise, cites Indian diesel quality standards (BIS VI); for (b): critiques water as ideal fluid—cheap and safe but high critical pressure limits thermal efficiency; for (d): identifies absorption systems for solar cooling in Indian rural areas and waste heat recovery in process industries; for (e): comments on comfort conditions and HVAC design implications for hot-humid Indian climates.	Brief mention of practical relevance for each part—diesel knock mentioned, some working fluid examples given, absorption for waste heat noted; superficial connection to Indian context.	No practical interpretation—treats all parts as purely academic exercises; no mention of engine performance, power plant economics, refrigeration applications, or air-conditioning relevance; missing connection to engineering practice.

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