--- title: "Simple vapour compression cycle" subject: "Applied Thermodynamics" chapter: 3 key: "semester_3/applied_thermodynamics:simple-vcr-cycle-ts-ph-diagrams" source: https://www.bctengineer.com/q/semester_3/applied_thermodynamics/simple-vcr-cycle-ts-ph-diagrams site: BCT Engineering --- # Simple vapour compression cycle Applied Thermodynamics · Chapter 3: Refrigeration - Asked in: year not given, 8 marks - Video: [Refrigeration Cycle (Vapor Compression Cycle) - with Animation and Technically Correct](https://www.youtube.com/watch?v=8paWhATWxgU) — AEC Learn - Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14 - Page: https://www.bctengineer.com/q/semester_3/applied_thermodynamics/simple-vcr-cycle-ts-ph-diagrams - Whole chapter: https://www.bctengineer.com/md/semester_3/applied_thermodynamics/chapter-3 ## Question With a neat sketch of the components, explain the working of a simple vapour compression refrigeration cycle. Represent the cycle on T-s and p-h diagrams and write the expressions for refrigerating effect, compressor work and COP. ## Short answer The simple vapour compression cycle comprises compressor, condenser, expansion valve, and evaporator. The ideal cycle involves isentropic compression (1-2), constant-pressure condensation (2-3), throttling (3-4), and constant-pressure evaporation (4-1). Refrigerating effect: h1-h4; compressor work: h2-h1; COP = (h1-h3)/(h2-h1). ## Answer The **simple vapour compression cycle** uses a refrigerant that evaporates at low pressure (absorbing heat from the cold space) and condenses at high pressure (rejecting heat to the surroundings). ```text Q_H (heat rejected) +------------------+ 2 -->| CONDENSER |--> 3 +------------------+ ^ | | v COMPRESSOR <-- W EXPANSION VALVE ^ | | v +------------------+ 1 <--| EVAPORATOR |<-- 4 +------------------+ Q_L (heat absorbed) ``` #### Processes (ideal cycle) - **1-2 Isentropic compression:** dry saturated vapour at $p_e$ is compressed to superheated vapour at $p_c$. - **2-3 Condensation at constant pressure:** the vapour is desuperheated and condensed to saturated liquid, rejecting $Q_H$. - **3-4 Throttling (isenthalpic):** liquid expands in the expansion valve or capillary tube, $h_3 = h_4$; some flashes to vapour; the temperature falls to the evaporator value. - **4-1 Evaporation at constant pressure:** the wet mixture takes heat $Q_L$ from the cold space and becomes dry saturated vapour. #### Diagrams ```text T-s diagram p-h diagram T p | 2 | 3------------2 | / | | | / | 3-----2' | | | / | | | | | / | 4--------1 | 4------1 +-------------- s +----------------- h ``` In the T-s diagram 3-2' is condensation, 2'-2 is desuperheating and 1-2 is vertical (isentropic). On the p-h diagram, lines 4-1 and 2-3 are horizontal, 3-4 is vertical (constant enthalpy) and 1-2 follows a constant-entropy line sloping upward. #### Performance expressions (per kg) $$ \begin{aligned} q_L &= h_1 - h_4 = h_1 - h_3\quad\text{(refrigerating effect)}\\ w &= h_2 - h_1\quad\text{(compressor work)}\\ q_H &= h_2 - h_3\\ \text{COP} &= \frac{h_1 - h_3}{h_2 - h_1} \end{aligned} $$ Mass flow for a capacity $Q$: $\dot m = Q/(h_1 - h_4)$ and power $P = \dot m (h_2 - h_1)$. ## Check yourself The answer's key points as multiple-choice questions, with the correct option and why. 1. Process 1-2 in the ideal cycle is A. isenthalpic throttling B. isentropic compression of dry saturated vapour to superheated vapour C. constant pressure condensation D. constant pressure evaporation Answer: B. The compressor raises pressure from the evaporator to the condenser pressure. (Key point: Compression) 2. In the expansion valve the refrigerant undergoes A. isentropic expansion B. constant pressure heat rejection C. throttling at constant enthalpy (h3 = h4) D. isothermal compression Answer: C. Throttling is isenthalpic; some liquid flashes and temperature falls. (Key point: Throttling) 3. The refrigerating effect per kg is A. h2 - h1 B. h2 - h3 C. h2 - h4 D. h1 - h4 (= h1 - h3) Answer: D. Heat absorbed in the evaporator. (Key point: Refrigerating effect) 4. The COP is A. (h1 - h3)/(h2 - h1) B. (h2 - h1)/(h1 - h3) C. (h2 - h3)/(h2 - h1) D. (h1 - h3)/(h2 - h3) Answer: A. Refrigerating effect over compressor work. (Key point: COP) ## Related in Applied Thermodynamics - [Ideal vapour compression cycle for 5 TR](https://www.bctengineer.com/question.md?key=semester_3%2Fapplied_thermodynamics%3Avcr-ideal-cycle-numerical) — Applied Thermodynamics, chapter 3 - [Ideal versus actual vapour compression cycle](https://www.bctengineer.com/question.md?key=semester_3%2Fapplied_thermodynamics%3Aideal-vs-actual-vcr-cycle) — Applied Thermodynamics, chapter 3 - [Actual VCR cycle with compressor efficiency](https://www.bctengineer.com/question.md?key=semester_3%2Fapplied_thermodynamics%3Avcr-actual-compressor-efficiency-numerical) — Applied Thermodynamics, chapter 3 - [Refrigeration, TR, COP and applications](https://www.bctengineer.com/question.md?key=semester_3%2Fapplied_thermodynamics%3Arefrigeration-definition-applications) — Applied Thermodynamics, chapter 3 - [Work of single-stage compressor without clearance](https://www.bctengineer.com/question.md?key=semester_3%2Fapplied_thermodynamics%3Asingle-stage-compressor-work-derivation) — Applied Thermodynamics, chapter 2 - [VCR cycle with subcooling and superheating](https://www.bctengineer.com/question.md?key=semester_3%2Fapplied_thermodynamics%3Avcr-subcooling-superheating-numerical) — Applied Thermodynamics, chapter 3 ## Related in other subjects - [Vapour compression refrigeration cycle](https://www.bctengineer.com/question.md?key=semester_6%2Findustrial_power_distribution_and_illumination%3Avapour-compression-refrigeration) — Industrial Power Distribution and Illumination, chapter 5 - [Power vs refrigeration cycle; Rankine components and diagrams](https://www.bctengineer.com/question.md?key=semester_2%2Ffundamental_of_thermodynamics_and_heat_transfer%3Apower-vs-refrigeration-cycle-rankine-components) — Fundamental of Thermodynamics & Heat Transfer, chapter 6 - [Vapor compression refrigeration cycle p-h and T-s](https://www.bctengineer.com/question.md?key=semester_2%2Ffundamental_of_thermodynamics_and_heat_transfer%3Avapor-compression-refrigeration-ph-ts) — Fundamental of Thermodynamics & Heat Transfer, chapter 6 - [Three-process gas cycle: net work and heat](https://www.bctengineer.com/question.md?key=semester_2%2Ffundamental_of_thermodynamics_and_heat_transfer%3Athree-process-cycle-pv-const-800kpa) — Fundamental of Thermodynamics & Heat Transfer, chapter 4