22-Mec-A1 Applied Thermodynamics and Heat Transfer · May 2017
Question 4 of 8: Ammonia Vapour-Compression Refrigeration Plant
Nivaar worked solution (AI-drafted; not reviewed by a licensed engineer)
Notes on this paper
Reference texts: Çengel & Boles, Thermodynamics: An Engineering Approach (9th ed., McGraw-Hill) — closed- and open-system energy balances, filling of evacuated vessels, air-standard dual and gas-turbine (turbojet) cycles, and vapour-compression refrigeration; Çengel & Ghajar, Heat and Mass Transfer (6th ed.) and Incropera, DeWitt, Bergman & Lavine, Fundamentals of Heat and Mass Transfer (8th ed., Wiley) — radial composite-cylinder conduction with convection, external cross-flow over a cylinder, internal-flow temperature decay, radiation between concentric spheres with a shield, and the ε–NTU cross-flow heat-exchanger method. Ammonia and ideal-gas air properties are read from the tables appended to the examination paper; the turbojet uses cold-air-standard constant specific heats.
Paper format: National Examination 16-Mec-A1, May 2017, 3 hours, open book. Part A — Thermodynamics (Q1–4); Part B — Heat Transfer (Q5–8). Each answer carries equal value; a complete paper is any five (three questions from one part and two from the other). All eight questions are solved in full below.
250 kPa, −10 °C (superheated ~3.7 °C); $h_1\approx1429.9$ kJ/kg
Given duties
$\dot W_c=2.12$ kW, $\dot m=0.007$ kg/s
Given. The state and duty data above. Find. (a) the quality after the throttle, (b) the evaporator heat-absorption rate, (c) the coefficient of performance.
Figure 4 — Ammonia cycle on $T$–$s$ axes: 1→2 compression to 1200 kPa, 2→3 condensation + subcooling to 27 °C liquid, 3→4 isenthalpic throttle into the two-phase region at 250 kPa, 4→1 evaporation and slight superheat to −10 °C.
Approach. Fix the liquid enthalpy before the throttle (subcooled ≈ saturated liquid at 27 °C), carry it unchanged through the isenthalpic valve to find the quality at 250 kPa, take the evaporator exit enthalpy from the superheat table, and combine the given compressor work with the evaporator duty for the COP.
Enthalpy before and after the throttle. The liquid at 27 °C, 1200 kPa is compressed liquid; $h_3\approx h_f(27\text{ °C})=308.4$ kJ/kg. Throttling is isenthalpic, so $h_4=h_3=308.4$ kJ/kg.
Quality after the throttle (250 kPa). At 250 kPa the saturation state ($T_{sat}=-13.67$ °C) has $h_f=118.4$, $h_{fg}=1308.9$ kJ/kg, so
$$x_4=\frac{h_4-h_f}{h_{fg}}=\frac{308.4-118.4}{1308.9}$$
$x_4\approx0.145$ (14.5 % vapour)
Evaporator exit enthalpy. At 250 kPa and −10 °C the ammonia is superheated ~3.7 °C above saturation; interpolating from $h_g$ at $-13.67$ °C toward the 0 °C superheat entry gives $h_1\approx1429.9$ kJ/kg.
Rate of heat absorbed in the evaporator. $\dot Q_L=\dot m(h_1-h_4)=0.007(1429.9-308.4)=0.007(1121.5)$.
$\dot Q_L\approx7.85$ kW (7.85 kJ/s)
Coefficient of performance. $\text{COP}=\dfrac{\dot Q_L}{\dot W_c}=\dfrac{7.85}{2.12}$.
$\text{COP}\approx3.70$
Check — table reads at the phase boundaries.
$h_3$ uses the compressed-liquid approximation $h\approx h_f(T)$ at 27 °C (subcooled ~4 °C below the 1200 kPa saturation of 30.96 °C). $h_1$ is a short extrapolation into superheat at 250 kPa (the table's first listed superheat point is 0 °C); a ±3 kJ/kg read shifts $\dot Q_L$ by ~0.3 % and the COP by ~0.01. A consistency check on the given data: $h_2=h_1+\dot W_c/\dot m=1732.7$ kJ/kg lands at ~150 °C on the 1200 kPa superheat table, a realistic ammonia discharge temperature.
