Thermodynamics visualizer

A kinetic-theory gas box with real measured pressure from actual particle collisions, and a piston sandbox for the four classic PV processes.

Lessons

Pick a topic, read the steps, then try them right in the sandbox below.

Class 11 — Kinetic theory: where pressure actually comes from

Concept: gas pressure isn't magic — it's the real, measurable result of countless particles colliding with the container walls. More particles or higher temperature (faster particles) means more, harder collisions, which means more pressure.

Switch to Kinetic theory gas mode.
Note the starting Pressure (measured) value.
Raise Temperature T and watch the particles visibly speed up — Pressure (measured) should rise too.
Reset the temperature, then instead raise Particles N — pressure rises again, this time because more particles are hitting the walls, not because they're faster.
Finally, drag the Piston (volume) control to shrink the box — pressure rises sharply as the same particles now hit the walls far more often.

Takeaway: pressure isn't one single "thing" — it's the combined effect of how many particles there are, how fast they're moving, and how much space they have.

Class 11 — The four PV processes

Concept: the same gas can be compressed or expanded in different ways — keeping temperature fixed (isothermal), pressure fixed (isobaric), volume fixed (isochoric), or with no heat exchange at all (adiabatic) — and each one does a different amount of work, shown as the area under the curve on the PV diagram.

Switch to PV diagram mode.
Select isothermal and drag Volume V to expand the gas. Note the Work done W=∫PdV value.
Reset, select adiabatic instead, and expand the volume by the same amount. Compare the work done — an adiabatic expansion does less work for the same volume change, because the gas cools as it expands instead of drawing in heat to stay at constant temperature.
Try isochoric (volume fixed) — confirm the work done stays at zero no matter what you do to Temperature, since W = ∫PdV needs the volume to actually change.

Takeaway: "work done by a gas" always means the area under its path on a PV diagram — and that area depends entirely on which of the four processes it follows.

The physics behind it

Formulas used in this lab

Ideal gas and kinetic theory Class 11

Ideal gas law: PV = nRT = Nk_BT
Pressure from molecular motion: P = (1/3)(N/V) m⟨v²⟩
Average kinetic energy per molecule: ½m⟨v²⟩ = (3/2)k_BT
rms speed: v_rms = √(3k_BT/m) = √(3RT/M)
Gas laws: Boyle: PV = const (T fixed); Charles: V/T = const (P fixed); Gay-Lussac: P/T = const (V fixed)
In the box lab: P ∝ NT/V: more particles, a hotter gas or a smaller volume all raise the pressure

First law and the four processes Class 11

First law: Q = ΔU + W, W = ∫ P dV (area under the PV curve)
Internal energy of an ideal gas: ΔU = nC_vΔT, C_p − C_v = R, γ = C_p/C_v (1.4 here)
Isothermal (T constant): PV = const, ΔU = 0, W = nRT ln(V₂/V₁)
Isobaric (P constant): V/T = const, W = PΔV
Isochoric (V constant): P/T = const, W = 0, Q = ΔU
Adiabatic (Q = 0): PV^γ = const, TV^γ−1 = const, W = (P₁V₁ − P₂V₂)/(γ − 1)
Adiabatic vs isothermal: the adiabatic curve is steeper on a PV diagram