Ideal Gas Law

Use the simulator above to explore the relationship between pressure, volume, temperature, and moles of gas. Unlike a lot of the other simulators, this one has three different modes worth exploring separately: Explore (playing with the variables directly), Cycle (watching a full thermodynamic cycle unfold step by step), and Challenge (solving word problems with the gas laws).

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How to Use the Ideal Gas Law Simulator

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View

Use the Dark mode toggle to switch between light and dark themes for the particle box.

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Explore Mode

Process Type lets you constrain how the gas is allowed to change: Free (no constraint), Isothermal (temperature held constant), Isobaric (pressure held constant), or Isochoric (volume held constant).

Calculating lets you choose which of the four variables (P, V, T, n) is solved for you based on the other three — the sliders for the other three become your inputs, and the selected one updates automatically.

Note for teachers: switching which variable is "Calculating" is a good way to show students that PV = nRT isn't just solved for one variable — any of the four can be the unknown depending on the problem.

The equation panel below the sliders shows the full calculation in real time (P × V vs. n × R × T) and puts a checkmark next to it once both sides agree, which they always will here — it's a live proof that the relationship holds, not a check on a guess.

Show pressure arrows toggles the little arrows around the box that represent gas pressure pushing outward on the walls.

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Cycle Mode

Choose a cycle to run: Carnot-like Cycle (two isothermal legs plus two isochoric legs, used to introduce ideal efficiency), Rectangular Cycle (two isobaric legs plus two isochoric legs, whose net work is just the area of the rectangle on the P-V diagram), or Custom Cycle (click directly on the P-V diagram to place your own state points and build a cycle from scratch).

Note for teachers: Custom Cycle is the one to use if you want students to discover for themselves that net work equals the enclosed area on a P-V diagram, rather than being told that fact up front.

Click Start Cycle (or Step 1, Step 2, etc. once it's running) to advance leg by leg. Each leg shows the work done, the change in internal energy, and the heat absorbed or rejected, so you can watch the first law of thermodynamics balance out one step at a time.

The P-V diagram in the corner plots the actual path the gas is taking through the cycle, which updates as you step through it.

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Challenge Mode (Test your understanding!)

Difficulty: Easy or Hard.

Easy: word problems solved directly with PV = nRT.

Hard: pulls in the ratio laws (Boyle's, Charles's, Gay-Lussac's, Combined Gas Law), Dalton's Law of partial pressures, and STP problems — a noticeably bigger jump than Easy, not just harder numbers.

Quiz mode chains multiple challenges back-to-back instead of stopping after one, if you want a running set for students to work through.

A "Given" panel lists the known values from the word problem, and "Find" tells you which one you're solving for.

Mastery tip: read the word problem itself before looking at the Given panel — figuring out which law applies from the situation described is most of the challenge here, not the algebra.

Enter your answer and click Check. Submitting an answer reveals a worked hint showing the calculation, regardless of whether you got it right.

Print Challenge exports the current problem if you want a paper copy for a student, a sub, or a bell-ringer.