25-Nav-A1 Fundamentals of Naval Architecture · May-98-Mar-A1 2016
Question 4 of 8: Actual Freon-12 Vapour-Compression Refrigeration Cycle
Nivaar worked solution (AI-drafted; not reviewed by a licensed engineer)
Notes on this paper
National Examinations, May 2016 — 98-Mar-A1 Applied Thermodynamics and Heat Transfer, 3 hours, open book (Part A: Thermodynamics, Part B: Heat Transfer; 5 of 8 questions required, all 8 answered below for full study coverage).
Reference texts: Cengel & Boles, Thermodynamics: An Engineering Approach; Sonntag, Borgnakke & Van Wylen, Fundamentals of Thermodynamics; Incropera & DeWitt, Fundamentals of Heat and Mass Transfer.
It is solved as the thermodynamics/heat-transfer exam it actually is.
Question 4: Actual Freon-12 Vapour-Compression Refrigeration Cycle
Given. Real (non-adiabatic, non-isentropic) R-12 cycle from plant test data — the compressor loses heat, and there is measurable superheat/subcooling at several points.
Given data
Location
Pressure
Temperature
Compressor inlet
150 kPa
0°C
Compressor outlet
700 kPa
70°C
Condenser inlet
700 kPa
60°C
Condenser outlet
700 kPa
15°C
Expansion-valve inlet
700 kPa
20°C
Evaporator outlet
150 kPa
−10°C
Find. Coefficient of performance $COP$ and the isentropic efficiency of the compression process, given $q_{loss}=3.35\text{ kJ/kg}$ during compression.
Actual R-12 cycle on the T–s plane, read directly from the given test-data states (1: compressor inlet, 2: compressor outlet, 3: condenser inlet, 4/4': condenser/liquid-line exit, 5: evaporator outlet).
Approach. Read enthalpies at each measured state from the R-12 saturation/superheat tables, form the actual compressor work from an energy balance that includes the heat loss, then get $q_L$ and $COP$; compare against the isentropic compressor work for the second part.
Enthalpies from the tables. Compressor inlet (0.15 MPa, 0°C): $h_1=190.66\text{ kJ/kg}$, $s_1=0.7543\text{ kJ/kg}\cdot\text{K}$. Compressor outlet (0.70 MPa, 70°C): $h_2=228.93\text{ kJ/kg}$. Evaporator outlet (0.15 MPa, −10°C): $h=184.62\text{ kJ/kg}$. Expansion-valve inlet, saturated-liquid approximation at 20°C: $h\approx54.83\text{ kJ/kg}$ (this equals the evaporator-inlet enthalpy after throttling, $h_3=h_4$).
Actual compressor work. Energy balance with heat lost during compression, $w_{in}=(h_2-h_1)+q_{loss}$:
$$w_{comp}=(228.93-190.66)+3.35=38.27+3.35\approx41.62\text{ kJ/kg}$$
Refrigerating effect and COP. $q_L=h_{evap,out}-h_{throttle,out}=184.62-54.83=129.79\text{ kJ/kg}$:
$$\boxed{COP=\frac{q_L}{w_{comp}}=\frac{129.79}{41.62}\approx3.12}$$
Isentropic efficiency of compression. At 0.70 MPa with $s=s_1=0.7543$, interpolating between the 50°C and 60°C table rows gives $h_{2s}\approx220.32\text{ kJ/kg}$, so $w_{isen}=h_{2s}-h_1=29.66\text{ kJ/kg}$:
$$\boxed{\eta_{isen}=\frac{w_{isen}}{w_{comp}}=\frac{29.66}{41.62}\approx71.2\%}$$
