(a) The following data refers to a single-stage vapour compression refrigeration system : Refrigerant = R134a Condenser…

(a)(i) – (v)

P–h diagram (drawn below): P vertical (log scale), h horizontal. States: 1 dry saturated vapour at 2.014 bar; 2s isentropic compression at 8.870 bar; 2 actual compression; 3 after condensation and 5 °C subcooling; 4 after isenthalpic throttling at 2.014 bar. Process lines: 4–1 evaporation, 1–2 actual compression (1–2s dashed isentropic), 2–3 condensation/subcooling, 3–4 throttling.

State 1: h₁ = 392.4 kJ/kg, s₁ = 1.733 kJ/kg·K, v₁ = 0.0994 m³/kg.

Volumetric efficiency: p₂/p₁ = 8.870/2.014 = 4.4042, so η_v = 1 + C − C(p₂/p₁)^(1/n) = 1.03 − 0.03 × (4.4042)^(1/1.12) = 1.03 − 0.03 × 3.7573 = 0.9173.

Mass flow: swept-volume rate = 269.4 × 10⁻⁶ × 2800/60 = 0.012572 m³/s, so ṁ = η_v V̇_s/v₁ = 0.9173 × 0.012572/0.0994 = 0.1160 kg/s.

Isentropic compression: s₂ₛ = s₁ = 1.733 > s_g(8.87 bar) = 1.715, so state 2s is superheated. With c_p,v = 1.1 kJ/kg·K, T₂ₛ = 308.15 × exp[(1.733 − 1.715)/1.1] = 313.23 K, and h₂ₛ = 417.6 + 1.1 × (313.23 − 308.15) = 423.19 kJ/kg.

Actual compression: h₂ = h₁ + (h₂ₛ − h₁)/η_c = 392.4 + 30.79/0.75 = 433.45 kJ/kg, so w_c = 41.05 kJ/kg (discharge temperature ≈ 49.4 °C).

Subcooling and throttling: h₃ = h_f(35 °C) − c_p,l × 5 = 249.1 − 1.458 × 5 = 241.81 kJ/kg = h₄, so q_e = h₁ − h₄ = 150.59 kJ/kg.

(i) Capacity: Q_e = ṁq_e = 0.1160 × 150.59 = 17.47 kW = 4.97 TR (1 TR = 3.5167 kW).

(ii) Power: W = ṁw_c = 0.1160 × 41.05 = 4.76 kW.

(iii) COP = q_e/w_c = 150.59/41.05 = 3.67.

(iv) Heat rejected in the condenser: Q_c = ṁ(h₂ − h₃) = 0.1160 × (433.45 − 241.81) = 22.23 kW, which equals Q_e + W as a check.

(v) Second-law efficiency: COP_Carnot = T_L/(T_H − T_L) = 263.15/45 = 5.848, so η_II = 3.67/5.848 = 0.627 (62.7%).

(b)(i)

Important lubricant properties in IC engines:

• Viscosity: maintains oil film; too high causes pumping loss, too low causes wear.
• Viscosity index: low change of viscosity with temperature; ensures cold starting and hot protection.
• Pour point: must be low for cold-weather flow.
• Flash and fire point: high for safety and low evaporation loss.
• Oxidation and thermal stability: resist sludge, varnish and thickening at high temperature.
• Detergency and dispersancy: keep soot and deposits suspended, keeping engine clean.
• Anti-wear and extreme-pressure properties: protect cams, bearings and piston rings in boundary lubrication.
• Corrosion and rust inhibition: neutralise acidic combustion products.
• Foam resistance: prevents air entrainment and oil-film breakdown.
• Seal compatibility: prevents swelling, shrinkage and leakage.
• Alkalinity/TBN: neutralises acids and extends drain interval. Significance: together these ensure lubrication, cooling, sealing, cleaning, corrosion protection and longer engine life.

(b)(ii)

Advantages of IDI swirl chamber over open DI: lower injection pressure is needed; better fuel-air mixing at low speed and part load; smoother pressure rise, lower combustion noise; lower NOx due to lower peak temperature; less sensitive to fuel quality; wider speed range for small engines. Disadvantages: higher specific fuel consumption, often 10–20% penalty, because of heat loss and throttling between chambers; lower thermal efficiency and power output; more complex cylinder head and higher manufacturing cost; poorer cold starting, needing glow plugs; greater heat loss and thermal loading; limited to smaller engines; poorer full-load economy than open DI.

(c)

For steam, use isentropic expansion index n = 1.135. Critical pressure ratio: p*/p₁ = (2/(n+1))^(n/(n−1)) = (2/2.135)^(1.135/0.135) = 0.5774. p₁ = 10 bar, so p* = 10 × 0.5774 = 5.774 bar. Critical pressure = 5.77 bar.

From saturated steam tables at 10 bar dry saturated: v₁ = v_g = 0.1944 m³/kg. Critical velocity: c* = √[2n/(n+1) p₁v₁] = √[(2×1.135/2.135) × 10×10⁵ × 0.1944] = √(1.0632 × 1.944×10⁵) = 454.6 m/s.

Specific volume at throat: v* = v₁(p₁/p*)^(1/n) = 0.1944(1/0.5774)^(1/1.135) = 0.3155 m³/kg. Throat area per unit mass flow rate: A*/ṁ = v*/c* = 0.3155/454.6 = 6.94×10⁻⁴ m² per (kg/s). **A*/ṁ = 6.94 cm² per kg/s.**