---
title: "The First Law of Thermodynamics for Any Process"
description: "Internal energy changes only by heat added and work done, whatever route the system takes. Applying it means being careful about signs and about which quantities depend on the path."
canonical: https://lightmysky.com/learn/science/the-first-law-of-thermodynamics-for-any-process-mt_LIWgeWSXHz
source: https://lightmysky.com/learn/science/the-first-law-of-thermodynamics-for-any-process-mt_LIWgeWSXHz.md
retrieved: 2026-09-12
---

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# The First Law of Thermodynamics for Any Process

Internal energy changes only by heat added and work done, whatever route the system takes. Applying it means being careful about signs and about which quantities depend on the path.

Subject: Science · Area: Thermal & Statistical Physics · Ages 18 to 19
Page: https://lightmysky.com/learn/science/the-first-law-of-thermodynamics-for-any-process-mt_LIWgeWSXHz

## Ready when they can

- States the first law with a consistent sign convention and applies it to a stated process
- Explains why internal energy is a state function while heat and work are not
- Traces energy round a complete cycle and shows the internal energy change is zero

## Lesson: Energy in, energy out: the first law

The first law says the change in internal energy equals the heat added minus the work done by the system. Energy never appears from nothing. Fix one sign rule, with work by the system counting positive, and keep it for every term.

Internal energy is fixed by the current state alone, so it is a state function. Heat and work describe the route taken, so the same endpoints can pair with many values of each.

**Example.** Squeeze a gas while it loses heat and two effects fight: the squeeze pushes energy in while the leaking heat drains it, and the change in internal energy is the balance. Heating at fixed volume sends every joule into internal energy, since no boundary work happens, while heating at fixed pressure spends part on work. With no heat flow at all, called adiabatic, any work comes straight from internal energy and the temperature shifts.

**Tip.** Round a full cycle the internal energy change is zero, so the net heat in equals the net work out. Trace each leg with its sign and the loop must balance.

**Recap.** Heat in minus work out sets the change inside, and loops always balance to zero.

## Practice

8 questions on this page, each with its working shown.

## Needs first

- [Thermodynamic State Variables and PV Diagrams](https://lightmysky.com/learn/science/thermodynamic-state-variables-and-pv-diagrams-mt_G3EYx84GZK)
- [Internal Energy, Absolute Zero and the Kelvin Scale](https://lightmysky.com/learn/science/internal-energy-absolute-zero-and-the-kelvin-scale-mt_n4Ku8ZDy1U)

## Opens up

- [Work in Isothermal, Isobaric and Adiabatic Processes](https://lightmysky.com/learn/science/work-in-isothermal-isobaric-and-adiabatic-processes-mt_WzVxwN3svc)