--- title: "Work in Isothermal, Isobaric and Adiabatic Processes" description: "Each idealised process fixes one variable and gives its own expression for the work, with the adiabatic case following a steeper curve than the isothermal one. Which curve applies decides how much a c" canonical: https://lightmysky.com/learn/science/work-in-isothermal-isobaric-and-adiabatic-processes-mt_WzVxwN3svc source: https://lightmysky.com/learn/science/work-in-isothermal-isobaric-and-adiabatic-processes-mt_WzVxwN3svc.md retrieved: 2026-09-12 --- > **Agent view.** This is the Markdown twin of the page, for tools and assistants. > When to use this site, and the call that answers each job: https://lightmysky.com/agent-instructions.md > API description (OpenAPI 3.1): https://lightmysky.com/openapi.json · Authentication: https://lightmysky.com/auth.md > Pricing: https://lightmysky.com/pricing.md · Catalog: https://lightmysky.com/llms.txt · Full catalog: https://lightmysky.com/llms-full.txt > Every machine-readable file on this domain: https://lightmysky.com/.well-known/ai-catalog.json > Ask for Markdown with `Accept: text/markdown`, a `.md` address, or `?mode=agent`. # Work in Isothermal, Isobaric and Adiabatic Processes Each idealised process fixes one variable and gives its own expression for the work, with the adiabatic case following a steeper curve than the isothermal one. Which curve applies decides how much a compressed gas heats up. Subject: Science · Area: Thermal & Statistical Physics · Ages 19 to 20 Page: https://lightmysky.com/learn/science/work-in-isothermal-isobaric-and-adiabatic-processes-mt_WzVxwN3svc ## Ready when they can - Derives the work done in isothermal and isobaric expansion by integration - Uses the adiabatic relation between pressure and volume and says where the exponent comes from - Explains why an adiabatic compression raises the temperature and an isothermal one does not ## Lesson: Each process has its own work rule Work is the area under the pV curve, which is the integral of p dV. At fixed pressure p slides out front, so isobaric work is p times delta V. At fixed temperature the integral gives n R T times the log of V2 over V1, and the ideal gas keeps its internal energy, so every joule of heat becomes work. **Example.** A car engine squeezes its fuel-air mix from 240 to 40 cubic cm with no heat flow. Pressure jumps from 1.00e5 to 1.23e6 and temperature climbs from 293 K to 600 K, costing about 63 J of compression work. The same squeeze done isothermally would stay at 293 K, with the work leaving as heat instead. Adiabatic means Q equals zero: p times V to the gamma stays constant, where gamma is Cp over Cv, about 1.4 for diatomic air. Because gamma tops one, the adiabat runs steeper than the isotherm on a pV plot. Compression work then has nowhere to go but inside, so the gas warms; expansion spends internal energy, so it cools. **Tip.** Name the process by what stays fixed: T for isothermal, p for isobaric, Q equals zero for adiabatic. Expanding into a vacuum does zero work, since it pushes against zero pressure. Watch signs: work the gas does counts positive in the integral. **Recap.** Isobaric work is p delta V, isothermal work is n R T log V2 over V1, and adiabatic work stays inside as temperature change. ## Practice 8 questions on this page, each with its working shown. ## Needs first - [The First Law of Thermodynamics for Any Process](https://lightmysky.com/learn/science/the-first-law-of-thermodynamics-for-any-process-mt_LIWgeWSXHz) ## Opens up - [Heat Engines and the Second Law](https://lightmysky.com/learn/science/heat-engines-and-the-second-law-mt_M7CDvIi4Vs)