---
title: "Thermodynamic process; isothermal expansion diagrams"
subject: "Fundamental of Thermodynamics & Heat Transfer"
chapter: 1
key: "semester_2/fundamental_of_thermodynamics_and_heat_transfer:process-sketch-isothermal-expansion"
source: https://www.bctengineer.com/q/semester_2/fundamental_of_thermodynamics_and_heat_transfer/process-sketch-isothermal-expansion
site: BCT Engineering
---

# Thermodynamic process; isothermal expansion diagrams

Fundamental of Thermodynamics & Heat Transfer · Chapter 1: Introduction

- Asked in: 2067 Mangsir, 5 marks
- Video: [Isothermal process Thermodynamics -  Work, Heat & Internal Energy, PV Diagrams](https://www.youtube.com/watch?v=m9h6qyWLscs) — The Organic Chemistry Tutor
- 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/process-sketch-isothermal-expansion
- Whole chapter: https://www.bctengineer.com/md/semester_2/fundamental_of_thermodynamics_and_heat_transfer/chapter-1

## Question

Define thermodynamic process. Sketch P-v, T-v and P-T diagram for an ideal gas undergoing isothermal expansion.

## Short answer

A thermodynamic process is the path of successive equilibrium states. For isothermal expansion: P-v diagram is a hyperbola (Pv=constant), T-v is horizontal, P-T is vertical.

## Answer

A **thermodynamic process** is the path of successive equilibrium states followed by a system as it changes from an initial to a final state, e.g. isobaric, isochoric, isothermal, adiabatic.

#### Isothermal expansion of an ideal gas
T = constant, so PV = mRT = constant: P = C/V (rectangular hyperbola). On expansion, v increases and P decreases.

```text
 P-v diagram        T-v diagram        P-T diagram
 P|                 T|                 P|  1
  |1                 |                  |  |
  | \                |1 ------> 2       |  |
  |  \_              |                  |  |
  |    \__ 2         |                  |  2
  +--------- v       +--------- v       +--------- T
 hyperbola Pv=C      horizontal line    vertical line
```

- P-v: falling hyperbola from 1 to 2, with v₂ > v₁ and P₂ < P₁; area under the curve = W = mRT ln(V₂/V₁).
- T-v: horizontal line at constant T.
- P-T: a vertical line (T constant, P falls from P₁ to P₂).

## Check yourself

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

1. For isothermal expansion of an ideal gas, P and V are related by
   A. P/V = constant
   B. PV = constant
   C. P V^1.4 = constant
   D. P is constant
   Answer: B. At constant T, PV = mRT is constant, so P = C/V. (Key point: Isothermal relation)

2. On a P-v diagram, isothermal expansion appears as
   A. a vertical line
   B. a horizontal line
   C. a falling rectangular hyperbola
   D. a rising straight line
   Answer: C. v increases and P decreases along Pv = C. (Key point: P-v diagram)

3. On a T-v diagram, the process is
   A. a vertical line
   B. a line through the origin
   C. a hyperbola
   D. a horizontal line
   Answer: D. T is constant, so the line is horizontal. (Key point: T-v diagram)

4. On a P-T diagram, the process is
   A. a vertical line, with P falling at constant T
   B. a horizontal line
   C. a line through the origin
   D. a hyperbola
   Answer: A. T stays fixed while P falls from P1 to P2, giving a vertical line. (Key point: P-T diagram)

## Related in Fundamental of Thermodynamics & Heat Transfer

- [Thermodynamic process; constant pressure heating diagrams](https://www.bctengineer.com/question.md?key=semester_2%2Ffundamental_of_thermodynamics_and_heat_transfer%3Aprocess-sketch-constant-pressure-heating) — Fundamental of Thermodynamics & Heat Transfer, chapter 1
- [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
- [Three-process gas cycle: net work, heat, type](https://www.bctengineer.com/question.md?key=semester_2%2Ffundamental_of_thermodynamics_and_heat_transfer%3Athree-process-cycle-pv-sketch) — Fundamental of Thermodynamics & Heat Transfer, chapter 4, asked 2×
- [Ideal Brayton cycle: diagrams and efficiency](https://www.bctengineer.com/question.md?key=semester_2%2Ffundamental_of_thermodynamics_and_heat_transfer%3Abrayton-cycle-efficiency-derivation) — Fundamental of Thermodynamics & Heat Transfer, chapter 6, asked 2×
- [Ideal Otto cycle diagrams and efficiency](https://www.bctengineer.com/question.md?key=semester_2%2Ffundamental_of_thermodynamics_and_heat_transfer%3Aotto-cycle-efficiency-compression-ratio) — Fundamental of Thermodynamics & Heat Transfer, chapter 6
- [Isentropic relations for ideal gas and incompressible](https://www.bctengineer.com/question.md?key=semester_2%2Ffundamental_of_thermodynamics_and_heat_transfer%3Aisentropic-process-relations) — Fundamental of Thermodynamics & Heat Transfer, chapter 5, asked 2×

## Related in other subjects

- [Ideal gas turbine with regenerator at 1400 K](https://www.bctengineer.com/question.md?key=semester_7%2Fpower_plant_equipment%3Agt-ideal-regenerator-1400k) — Power Plant Equipment, chapter 6
- [Practical vs ideal transformer, phasor diagram](https://www.bctengineer.com/question.md?key=semester_4%2Felectrical_machines%3Apractical-vs-ideal-transformer-phasor) — Electrical Machines, chapter 2
- [Heat treatment, objectives, isothermal annealing](https://www.bctengineer.com/question.md?key=semester_3%2Fcivil_engineering_materials%3Aheat-treatment-isothermal-annealing-s) — Civil Engineering Materials, chapter 8