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

# First law for control mass in cyclic process

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

- Asked in: 2071 Magh, 6 marks
- Video: [First law of thermodynamics | Chap 4 | control mass | TU/PU/KU/PoU](https://www.youtube.com/watch?v=xCFbUY207hk) — Sudip Dhakal
- 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-control-mass-cyclic
- Whole chapter: https://www.bctengineer.com/md/semester_2/fundamental_of_thermodynamics_and_heat_transfer/chapter-4

## Question

Explain the first law of thermodynamics for a control mass undergoing a cyclic process.

## Short answer

For a control mass undergoing a cycle, the net heat transfer equals the net work transfer: ∮ δQ = ∮ δW, i.e. Q_net = W_net. A perpetual motion machine of the first kind is impossible.

## Answer

#### First law for a control mass (closed system)
Energy cannot be created or destroyed; the net energy supplied to a closed system as heat and work equals the change in its energy:

**Q − W = ΔE = ΔU + ΔKE + ΔPE**

(Q into system +ve; W done by system +ve.)

#### Cyclic process
A cycle consists of processes which bring the system back to its initial state, so every property returns to its initial value:

ΔE = E_final − E_initial = 0

Hence  
**∮ δQ = ∮ δW**   or   **Q_net = W_net**

#### Statement
For a control mass undergoing a cycle, the net heat transfer to the system is equal to the net work done by the system. It is impossible to construct a machine that gives work without any energy supplied (perpetual motion machine of the first kind, PMM1).

#### Consequences
- Power cycle: W_net = Q_H − Q_L (positive).
- Refrigerator or heat pump: W_in = Q_H − Q_L (the system receives net work and rejects net heat).

```text
 P|    ___
  |   /   \   clockwise: W_net = + (power cycle)
  |   \___/   area = W_net = Q_net
  +--------- V
```

## Check yourself

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

1. First law for a closed system:
   A. Q - W = ΔU + ΔKE + ΔPE
   B. Q = ΔH
   C. Q + W = 0
   D. Q - W = Δh
   Answer: A. Energy is conserved. (Key point: Closed system)

2. In a cycle:
   A. Q_net = 0
   B. ΔE = 0, so Q_net = W_net
   C. W_net = 0
   D. ΔE = Q
   Answer: B. E is a property. (Key point: Cycle)

3. PMM1 is impossible because:
   A. Heat cannot flow cold to hot
   B. It violates the second law only
   C. A machine cannot give work without energy input
   D. Efficiency cannot exceed Carnot
   Answer: C. Violates the first law. (Key point: PMM1)

4. Which is a path function?
   A. Internal energy
   B. Total energy
   C. Enthalpy
   D. Heat and work
   Answer: D. E is a property; Q and W depend on path but Q - W does not. (Key point: Path functions)

## Close variants set in other exams

- [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×

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