---
title: "Work and heat transfer; sign conventions"
subject: "Fundamental of Thermodynamics & Heat Transfer"
chapter: 2
key: "semester_2/fundamental_of_thermodynamics_and_heat_transfer:work-heat-sign-conventions"
source: https://www.bctengineer.com/q/semester_2/fundamental_of_thermodynamics_and_heat_transfer/work-heat-sign-conventions
site: BCT Engineering
---

# Work and heat transfer; sign conventions

Fundamental of Thermodynamics & Heat Transfer · Chapter 2: Energy and Energy Transfer

- Asked in: 2067 Mangsir, 4 marks
- Video: [Thermo 2.6 - Heat and Work Sign Convention and Path Dependance](https://www.youtube.com/watch?v=RgPLbYhfBYw) — Rasim Guldiken
- 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/work-heat-sign-conventions
- Whole chapter: https://www.bctengineer.com/md/semester_2/fundamental_of_thermodynamics_and_heat_transfer/chapter-2

## Question

Define work transfer and heat transfer. Also mention their sign conventions used in the analysis of thermodynamic problems.

## Short answer

Work is energy crossing boundary due to force; heat is energy from temperature difference. Standard sign convention: positive for heat added and work done by the system. First law for closed system: ΔU = Q − W.

## Answer

#### Work transfer
Work is the energy interaction between a system and its surroundings that crosses the boundary when a system moves under the action of a force; formally, it is done when the sole external effect on the surroundings could be the raising of a weight. Examples: displacement work P dV, shaft work, electrical work.

#### Heat transfer
Heat is the energy that crosses the boundary of a system because of a temperature difference between the system and the surroundings. It flows from the higher to the lower temperature by conduction, convection or radiation.

Both are transient, boundary phenomena and path functions (δQ, δW).

#### Sign conventions (standard)

| Quantity | Positive (+) | Negative (−) |
|---|---|---|
| Heat Q | Heat **added to** the system | Heat **rejected from** the system |
| Work W | Work **done by** the system on surroundings | Work **done on** the system |

```text
        Q in (+)           W out (+)
  ---------------> [SYSTEM] --------------->
        Q out (-)  <------  <------ W in (-)
```

With this convention the first law for a closed system is Q − W = ΔE, i.e. ΔU = Q − W for a stationary system.

## Check yourself

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

1. How is heat transfer defined?
   A. Energy crossing the boundary because of a temperature difference
   B. Energy crossing the boundary due to a force moving the boundary
   C. Energy stored in the system by its temperature
   D. Any energy flow including mass crossing the boundary
   Answer: A. Heat is boundary energy transfer driven by a temperature difference, from high to low temperature. (Key point: Definition of heat)

2. In the standard convention, which sign does work done by the system on the surroundings have?
   A. Negative
   B. Positive
   C. Zero
   D. Depends on whether heat is also added
   Answer: B. Work done by the system is positive and work done on the system is negative. (Key point: Work sign)

3. Heat rejected from the system is treated as what?
   A. Positive
   B. Positive, as it is energy leaving
   C. Negative
   D. Zero if the process is reversible
   Answer: C. Heat added is positive and heat rejected is negative. (Key point: Heat sign)

4. With this convention the closed-system first law for a stationary system is:
   A. Delta U = Q + W
   B. Delta U = W - Q
   C. Delta U = Q x W
   D. Delta U = Q - W
   Answer: D. Heat in raises energy, work out lowers it, so Delta U = Q - W. (Key point: First law form)

## Related in Fundamental of Thermodynamics & Heat Transfer

- [Entropy change for reversible heat and work transfer](https://www.bctengineer.com/question.md?key=semester_2%2Ffundamental_of_thermodynamics_and_heat_transfer%3Aentropy-reversible-heat-work) — Fundamental of Thermodynamics & Heat Transfer, chapter 5, asked 3×
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