---
title: "First law for cyclic process; power and refrigeration cycles"
subject: "Fundamental of Thermodynamics & Heat Transfer"
chapter: 4
key: "semester_2/fundamental_of_thermodynamics_and_heat_transfer:first-law-cyclic-power-refrigeration"
source: https://www.bctengineer.com/q/semester_2/fundamental_of_thermodynamics_and_heat_transfer/first-law-cyclic-power-refrigeration
site: BCT Engineering
---

# First law for cyclic process; power and refrigeration cycles

Fundamental of Thermodynamics & Heat Transfer · Chapter 4: First Law of Thermodynamics

- Asked in: 2074 Bhadra, 6 marks
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_2/fundamental_of_thermodynamics_and_heat_transfer/first-law-cyclic-power-refrigeration
- Whole chapter: https://www.bctengineer.com/md/semester_2/fundamental_of_thermodynamics_and_heat_transfer/chapter-4

## Question

Define a cycle. Explain first law of thermodynamics for control mass undergoing cyclic process. Write down statements of first law for power cycle and refrigeration cycle.

## Short answer

A cycle is a sequence of processes returning a system to its initial state, with zero net property change. First law for a cycle: net heat transfer equals net work (∮δQ = ∮δW). In a power cycle, W_net = Q_H - Q_L, efficiency η = W_net/Q_H. In a refrigeration cycle, work input W_in = Q_H - Q_L, COP_ref = Q_L/W_in.

## Answer

#### Cycle
A cycle is a series of processes in which a system starts from an initial state, passes through other states and returns to the initial state. All properties return to their initial values: ΔE = 0, ∮dP = 0 and so on. On a P-V diagram, a cycle is a closed curve.

#### First law for a control mass undergoing a cycle
The first law for a process is Q − W = ΔE. For a cycle, ΔE = 0 (E is a property), so

**∮ δQ = ∮ δW**   i.e. Q_net = W_net

The net heat transferred to the system in a cycle equals the net work done by it.

#### Power cycle
A cycle that produces net work from heat input (clockwise on P-V; e.g. a steam power plant). Heat Q_H is received from a high-temperature source and Q_L is rejected to a sink:

**W_net = Q_H − Q_L**   (W_net > 0), efficiency η = W_net/Q_H = 1 − Q_L/Q_H

#### Refrigeration (heat pump) cycle
A cycle that needs net work input to remove heat Q_L from a cold space and reject Q_H to a hot space (anticlockwise on P-V):

**W_in = Q_H − Q_L**   (W_net < 0)

COP of refrigerator = Q_L/W_in; COP of heat pump = Q_H/W_in.

```text
  Power cycle                 Refrigeration cycle
  Hot reservoir T_H           Hot reservoir T_H
       | Q_H                       ^ Q_H
       v                           |
     [ E ] --> W_net             [ R ] <-- W_in
       | Q_L                       ^ Q_L
       v                           |
  Cold reservoir T_L          Cold reservoir T_L
```

## Check yourself

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

1. A cycle is:
   A. A series of processes returning the system to its initial state, so ΔE = 0
   B. A process at constant energy
   C. A process with no heat
   D. A series ending at a new state
   Answer: A. All properties return to initial values. (Key point: Cycle)

2. For a cycle the first law gives:
   A. ∮δQ = 0
   B. ∮δQ = ∮δW
   C. ∮δW = 0
   D. ∮δQ = -∮δW always
   Answer: B. Because ΔE = 0. (Key point: First law for cycle)

3. For a power cycle:
   A. W_in = Q_H - Q_L
   B. W_net = Q_L - Q_H, anticlockwise
   C. W_net = Q_H - Q_L > 0, clockwise on P-V
   D. W_net = 0
   Answer: C. Net work is produced. (Key point: Power cycle)

4. COP of a refrigerator is:
   A. Q_H/W_in
   B. W_in/Q_L
   C. Q_L/Q_H
   D. Q_L/W_in
   Answer: D. Cooling effect per work input; heat pump uses Q_H/W_in. (Key point: COP)

## Related in Fundamental of Thermodynamics & Heat Transfer

- [First law for control mass; cycle; power and refrigeration](https://www.bctengineer.com/question.md?key=semester_2%2Ffundamental_of_thermodynamics_and_heat_transfer%3Afirst-law-control-mass-cycle) — Fundamental of Thermodynamics & Heat Transfer, chapter 4
- [First law for control mass in cyclic process](https://www.bctengineer.com/question.md?key=semester_2%2Ffundamental_of_thermodynamics_and_heat_transfer%3Afirst-law-control-mass-cyclic) — Fundamental of Thermodynamics & Heat Transfer, chapter 4, asked 2×
- [First law for control mass, cyclic process](https://www.bctengineer.com/question.md?key=semester_2%2Ffundamental_of_thermodynamics_and_heat_transfer%3Afirst-law-control-mass-derive-cyclic) — Fundamental of Thermodynamics & Heat Transfer, chapter 4, asked 2×
- [First law for cyclic process; CV mass and energy equations](https://www.bctengineer.com/question.md?key=semester_2%2Ffundamental_of_thermodynamics_and_heat_transfer%3Afirst-law-cyclic-mass-energy-cv) — Fundamental of Thermodynamics & Heat Transfer, chapter 4
- [Mass and energy equations for non-flow; cyclic process](https://www.bctengineer.com/question.md?key=semester_2%2Ffundamental_of_thermodynamics_and_heat_transfer%3Amass-energy-nonflow-cyclic-closed) — Fundamental of Thermodynamics & Heat Transfer, chapter 4
- [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