(a) The following data refers to a single-stage vapour compression refrigeration system :

Refrigerant = R134a
Condenser temperature = 35 °C
Evaporator temperature = – 10 °C
Compressor motor speed = 2800 r.p.m.
Clearance ratio = 0·03
Swept volume = 2

Question

(a) The following data refers to a single-stage vapour compression refrigeration system :

Refrigerant = R134a
Condenser temperature = 35 °C
Evaporator temperature = – 10 °C
Compressor motor speed = 2800 r.p.m.
Clearance ratio = 0·03
Swept volume = 269·4 cm³
Expansion index = 1·12
Compression isentropic efficiency = 75%
Condensate subcooling in condenser = 5 °C

Draw P-h diagram and determine the following :

(i) The capacity of the plant in TR
(ii) The power required in kW
(iii) The COP
(iv) The heat rejection to condenser
(v) The second law efficiency

The properties of R134a are given in the table :

| T (°C) | P (bar) | Specific volume of saturated vapour v_g (m³/kg) | Enthalpy (kJ/kg) h_f | h_g | Entropy (kJ/kg-K) s_f | s_g |
|--------|---------|-----------------------------------------------|----------------------|-----|----------------------|-----|
| – 10 | 2·014 | 0·0994 | 186·7 | 392·4 | 0·9512 | 1·733 |
| 35 | 8·870 | — | 249·1 | 417·6 | 1·1680 | 1·715 |

Assume specific heat of liquid and vapour at 8·87 bar as 1·458 kJ/kg-K and 1·1 kJ/kg-K, respectively. The refrigerant at entry to compressor is in dry saturated state. (20 marks)

(b) (i) What are the important properties of lubricants used in IC engines? Discuss their significance. (10 marks)

(ii) What are the advantages and disadvantages of the Indirect Injection (IDI) swirl chamber over the open-type Direct Injection (DI) combustion chamber in CI engines? (10 marks)

(c) Calculate the critical pressure and throat area per unit mass flow rate of a convergent-divergent nozzle, expanding steam from 10 bar and dry saturated, down to atmospheric pressure of 1 bar. Assume that the inlet velocity is negligible and that the expansion is isentropic.

Use Steam tables given at the end to get the steam data.

The value of isentropic expansion index may be taken as 1·135. (10 marks)

UPSC Answer Check · Accepted Answer

Calculate systematically across all three parts, allocating time proportional to marks: ~40% for part (a) refrigeration cycle with P-h diagram and five performance parameters, ~30% for part (b) descriptive IC engine lubrication and combustion chamber comparison, and ~30% for part (c) nozzle critical pressure and throat area derivation. Begin each part with stated assumptions, show all thermodynamic property lookups and interpolation, and conclude with clearly boxed final answers with units.
- Part (a): Correct P-h diagram with 5 process points (1: dry saturated at -10°C, 2: after compression, 3: saturated liquid at 35°C, 4: after subcooling to 30°C, 5: after expansion); account for isentropic efficiency, clearance ratio for actual mass flow, and expansion index for re-expansion work
- Part (a): Mass flow rate calculation using clearance ratio and swept volume with volumetric efficiency; refrigerating effect using h1 - h4 with subcooled liquid enthalpy
- Part (a): Second law efficiency calculation requires Carnot COP between actual evaporator and condenser temperatures, not the saturation temperatures
- Part (b)(i): Viscosity index, pour point, flash/fire point, oxidation stability, detergency/dispersancy, and alkalinity with significance for engine wear, cold starting, deposit control, and corrosion prevention
- Part (b)(ii): IDI swirl chamber advantages (quieter, lower injection pressure, better air utilization at part load) vs disadvantages (higher heat loss, lower thermal efficiency, cold starting problems) compared to open DI chamber
- Part (c): Critical pressure ratio for steam using γ = 1.135; throat area per unit mass flow using isentropic flow relations with steam table enthalpy values, not ideal gas assumption
- Part (c): Correct use of steam tables to find h1, h2 (isentropic to throat), and specific volume at throat conditions
- All parts: Consistent units (bar, kJ/kg, m³/kg, K), proper significant figures, and explicit statement of formulas before substitution

Dimension	Weight	Max marks	Excellent	Average	Poor
Concept correctness	20%	10	For (a): correctly identifies all 5 P-h diagram states including subcooled liquid and accounts for clearance volume re-expansion; for (b): distinguishes between SAE viscosity grades and API service categories, explains swirl chamber thermochemistry; for (c): applies correct critical pressure ratio formula for non-ideal steam with n=1.135, not γ=1.4	For (a): basic P-h diagram correct but misses subcooling effect or confuses clearance ratio with volumetric efficiency; for (b): lists lubricant properties without explaining significance; for (c): uses ideal gas γ=1.4 incorrectly	Fundamental errors: treats compression as isentropic ignoring 75% efficiency in (a); confuses SI and CI engine lubricant requirements in (b); applies Bernoulli instead of isentropic flow relations in (c)
Numerical accuracy	20%	10	Part (a): Capacity ~0.9-1.0 TR, Power ~0.9-1.0 kW, COP ~3.0-3.3, second law efficiency ~65-70% with correct mass flow ~0.003-0.0035 kg/s; Part (c): Critical pressure ~5.3-5.4 bar, throat area/mass flow ~0.001-0.0012 m²·s/kg; all intermediate values shown	Correct methodology but arithmetic slips in interpolation (e.g., h4 calculation using cp=1.458) or unit conversion errors (cm³ to m³); final answers within 10% of expected	Order of magnitude errors: TR in hundreds, COP <1 or >10, critical pressure ratio inverted; ignores clearance ratio effect on mass flow entirely
Diagram quality	20%	10	Part (a): Neat P-h diagram with pressure axis logarithmic, all 5 state points labelled with T and h values, processes correctly shown (isentropic compression, constant pressure condensation, subcooling, throttling, constant pressure evaporation); part (c): T-s or h-s diagram for nozzle showing critical point	P-h diagram drawn but axes unlabelled or linear P scale; missing subcooling line or throttling shown as curved; no nozzle diagram for part (c)	T-s diagram instead of P-h for refrigeration cycle; no diagram at all; or completely wrong processes (e.g., compression shown as constant volume)
Step-by-step derivation	20%	10	Shows: (a) volumetric efficiency with clearance, re-expansion work, actual enthalpy at state 2 using isentropic efficiency, subcooled enthalpy calculation; (b) structured comparison table for IDI vs DI; (c) derivation of critical pressure ratio from dp/dv=0, then throat velocity from energy equation, then area from continuity	Jumps to final formulas without derivation but shows all substitutions; or derives but skips key steps like isentropic h2s before actual h2	No derivation shown—only final answers stated; or incorrect formula sequence (e.g., calculates COP before finding power)
Practical interpretation	20%	10	For (a): comments on effect of clearance ratio on capacity, why second law efficiency <100%, and typical industrial COP benchmarks for R134a; for (b): relates lubricant properties to Indian climatic conditions (high VI for temperature variation) and IDI suitability for small Indian automotive diesels; for (c): discusses choked flow implications for steam turbine nozzle design	Brief mention of practical relevance without specifics; generic statements like 'important for efficiency'	No interpretation; treats all parts as pure calculation exercises; no connection to real refrigeration plants, engine operation, or steam power plants

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