An adiabatic process trades no heat with its surroundings (Q = 0): every joule of work done compressing the gas raises its internal energy directly. Combining the first law of thermodynamics with the ideal gas law gives P·V^γ = constant, where γ = C_p/C_v is the ratio of heat capacities — 1.40 for a diatomic gas like air (5 active degrees of freedom), 1.667 for a monatomic noble gas (3 translational only).
Because γ > 1, this curve is always steeper than the isothermal hyperbola P·V = constant through the same starting point — both are plotted so the gap is visible. The same relation gives the temperature swing directly: T = T₁·(V₁/V)^(γ-1). Compress the gas and T rises even though no heat was added — the counter-intuitive result behind a diesel engine igniting fuel from compression heat alone, and behind a rising, expanding air parcel cooling as it climbs.
- Higher γ (monatomic) — fewer ways to store energy internally, so the same compression produces a bigger temperature and pressure jump.
- Compression ratio V₁/V — the same lever a real engine's compression ratio uses to raise ignition temperature.
This is the flat 2D companion to the 3D adiabatic-process-lab simulation: the same P·V^γ relation and T = T₁·(V₁/V)^(γ-1) law, viewed as a piston-cylinder cross-section with a live P-V trace.