---
title: "VCR cycle with subcooling and superheating"
subject: "Applied Thermodynamics"
chapter: 3
key: "semester_3/applied_thermodynamics:vcr-subcooling-superheating-numerical"
source: https://www.bctengineer.com/q/semester_3/applied_thermodynamics/vcr-subcooling-superheating-numerical
site: BCT Engineering
---

# VCR cycle with subcooling and superheating

Applied Thermodynamics · Chapter 3: Refrigeration

- Asked in: year not given, 6 marks
- Video: [P - H & T - S Diagram for Sub Cooling | Refrigeration & Air Conditioning | Power Engineering | Gate](https://www.youtube.com/watch?v=VVFyAd0N490) — Impact Academy Official
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_3/applied_thermodynamics/vcr-subcooling-superheating-numerical
- Whole chapter: https://www.bctengineer.com/md/semester_3/applied_thermodynamics/chapter-3

## Question

A vapour compression refrigerator of 3 TR capacity uses R-134a. The vapour leaves the evaporator slightly superheated with $h_1 = 243.5$ kJ/kg and, after isentropic compression, has $h_2 = 280.5$ kJ/kg. The liquid leaves the condenser subcooled with $h_3 = 88.5$ kJ/kg. Calculate (a) the refrigerating effect, (b) the mass flow rate, (c) the compressor power, and (d) the COP. Compare the COP with that of the saturated cycle $h_1 = 239.16$, $h_2 = 275.39$, $h_3 = 95.47$ kJ/kg (COP = 3.97) and comment. Take 1 TR = 3.517 kW.

## Short answer

Refrigerating effect = 155.0 kJ/kg; mass flow rate = 0.0681 kg/s; compressor power = 2.52 kW; COP = 4.19. Compared to saturated cycle (COP 3.97), subcooling and superheating improved COP by 5.6%.

## Answer

Capacity: $Q_L = 3 \times 3.517 = 10.551$ kW. Throttling gives $h_4 = h_3 = 88.5$ kJ/kg.

#### (a) Refrigerating effect
$$
q_L = h_1 - h_4 = 243.5 - 88.5 = 155.0\ \text{kJ/kg}
$$

#### (b) Mass flow rate
$$
\dot m = \frac{10.551}{155.0} = 0.0681\ \text{kg/s}
$$

#### (c) Compressor power
$$
w = h_2 - h_1 = 280.5 - 243.5 = 37.0\ \text{kJ/kg}
$$

$$
P = 0.0681 \times 37.0 = 2.52\ \text{kW}
$$

#### (d) COP
$$
\text{COP} = \frac{155.0}{37.0} = 4.19
$$

#### Comment
The COP rises from 3.97 to 4.19, about 5.6 %. The refrigerating effect increased from 143.7 to 155.0 kJ/kg: subcooling lowered $h_3$ by 6.97 kJ/kg, and the superheat (taken as useful, inside the evaporator) raised $h_1$ by 4.34 kJ/kg. Meanwhile the compressor work rose only slightly, from 36.2 to 37.0 kJ/kg.

**Answer:** (a) 155 kJ/kg; (b) 0.0681 kg/s; (c) 2.52 kW; (d) 4.19.

## Check yourself

The answer's key points as multiple-choice questions, with the correct option and why.

1. The refrigerating effect is
   A. 37.0 kJ/kg
   B. 192.0 kJ/kg
   C. 143.7 kJ/kg
   D. h1 - h4 = 155.0 kJ/kg
   Answer: D. 243.5 - 88.5 = 155.0. (Key point: Refrigerating effect)

2. The mass flow rate for 3 TR is
   A. 0.0681 kg/s
   B. 0.681 kg/s
   C. 0.0122 kg/s
   D. 0.1224 kg/s
   Answer: A. 10.551/155.0 = 0.0681. (Key point: Mass flow)

3. The compressor power is
   A. about 10.5 kW
   B. about 2.52 kW
   C. about 25 kW
   D. about 0.25 kW
   Answer: B. 0.0681 x 37.0 = 2.52. (Key point: Power)

4. Why does the COP rise from 3.97 to 4.19?
   A. Compressor work falls greatly
   B. Mass flow increases
   C. Subcooling raises the refrigerating effect more than superheat raises the work
   D. Condenser pressure is reduced
   Answer: C. Refrigerating effect grew from 143.7 to 155.0 kJ/kg, work only from 36.2 to 37.0. (Key point: COP comment)

## 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
- [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
- [Effects of subcooling and superheating](https://www.bctengineer.com/question.md?key=semester_3%2Fapplied_thermodynamics%3Asubcooling-superheating-effects) — Applied Thermodynamics, chapter 3
- [Simple vapour compression cycle](https://www.bctengineer.com/question.md?key=semester_3%2Fapplied_thermodynamics%3Asimple-vcr-cycle-ts-ph-diagrams) — 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

## 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