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Solve VCR Cycle for R134a: Refrigeration Effect, Compressor Work, COP Calculation
Mechanical Engineering (Thermodynamics)
University (Undergraduate 2nd/3rd Year)
Question Content
A VCR system uses R134a as refrigerant. The evaporator temperature is -5°C and the condenser temperature is 35°C. Determine: i. Refrigeration effect per kg of refrigerant ii. Compressor work per kg of refrigerant iii. Coefficient of Performance (COP). Assume: Isentropic compression, Saturated vapour at evaporator exit, Saturated liquid at condenser exit
Correct Answer
i. 184.7 kJ/kg, ii. 27.1 kJ/kg, iii. 6.816
Detailed Solution Steps
1
Step 1: Retrieve refrigerant properties from R134a tables. At evaporator temp -5°C (saturated vapour), h₁ = 244.5 kJ/kg, s₁ = 0.926 kJ/kg·K. At condenser temp 35°C (saturated liquid), h₄ = h₃ = 106.7 kJ/kg.
2
Step 2: For isentropic compression, s₂ = s₁. At 35°C condenser temp, find h₂ at s₂=0.926 kJ/kg·K: h₂ = 271.6 kJ/kg.
3
Step 3: Calculate refrigeration effect: q_L = h₁ - h₄ = 244.5 - 106.7 = 184.7 kJ/kg.
4
Step 4: Calculate compressor work: w_c = h₂ - h₁ = 271.6 - 244.5 = 27.1 kJ/kg.
5
Step 5: Calculate COP: COP = q_L / w_c = 184.7 / 27.1 ≈ 6.816
Knowledge Points Involved
1
Vapour Compression Refrigeration (VCR) Cycle Basics
A standard 4-process thermodynamic cycle (evaporation, compression, condensation, throttling) used for refrigeration. Assumptions include isentropic compression, saturated states at evaporator/condenser exits, and isenthalpic throttling.
2
Refrigerant Property Tables
Tabulated thermodynamic properties (enthalpy h, entropy s) for refrigerants like R134a, indexed by temperature and saturation state (saturated vapour/liquid) or entropy for isentropic processes.
3
Refrigeration Effect Calculation
The amount of heat removed per unit mass of refrigerant, calculated as q_L = h₁ - h₄, where h₁ is enthalpy at evaporator exit and h₄ is enthalpy at throttling valve inlet.
4
Isentropic Compressor Work
Work input to the compressor for a reversible adiabatic (isentropic) process, calculated as w_c = h₂ - h₁, where h₂ is enthalpy at compressor exit matching the entropy of the inlet state.
5
Coefficient of Performance (COP) for Refrigeration
A measure of refrigeration cycle efficiency, defined as the ratio of refrigeration effect to compressor work input: COP = q_L / w_c.
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