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R134a VCR Cycle Calculation: 0°C Evaporator, 40°C Condenser
Mechanical Engineering (Thermodynamics)
University (Undergraduate 2nd/3rd Year)
Question Content
A VCR system uses R134a as refrigerant. The evaporator temperature is 0°C, and the condenser temperature is 40°C. Refrigerant leaves the evaporator as saturated vapour and leaves the condenser as saturated liquid. The compression is isentropic. Determine: Refrigeration effect per kg, Compressor work per kg, COP
Correct Answer
i. 177.2 kJ/kg, ii. 28.6 kJ/kg, iii. 6.196
Detailed Solution Steps
1
Step 1: Retrieve R134a properties. At 0°C (saturated vapour), h₁ = 247.2 kJ/kg, s₁ = 0.919 kJ/kg·K. At 40°C (saturated liquid), h₄ = h₃ = 118.2 kJ/kg.
2
Step 2: For isentropic compression, s₂ = s₁. Find h₂ at 40°C condenser pressure and s₂=0.919 kJ/kg·K: h₂ = 275.8 kJ/kg.
3
Step 3: Refrigeration effect: q_L = h₁ - h₄ = 247.2 - 118.2 = 177.2 kJ/kg.
4
Step 4: Compressor work: w_c = h₂ - h₁ = 275.8 - 247.2 = 28.6 kJ/kg.
5
Step 5: COP = q_L / w_c = 177.2 / 28.6 ≈ 6.196
Knowledge Points Involved
1
VCR Cycle State Points
Defines the 4 key states of the cycle: 1 (evaporator exit, saturated vapour), 2 (compressor exit, superheated vapour), 3 (condenser exit, saturated liquid), 4 (throttling valve exit, two-phase mixture).
2
Isentropic Process Assumption
A reversible, adiabatic process where entropy remains constant (s₁ = s₂), used to simplify compressor work calculations for ideal cycle analysis.
3
Enthalpy Change in Throttling
Throttling valves are isenthalpic, so the enthalpy of saturated liquid at condenser exit equals the enthalpy of the two-phase mixture at evaporator inlet (h₃ = h₄).
4
COP for VCR Cycles
The ratio of useful refrigeration effect to the work input required, a key metric for evaluating refrigeration system efficiency.
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