Chemistry / thermodynamics / a visible equation
Find the missing pressure, volume, amount or temperature. Then change one condition and watch an ideal gas move along a clearly defined path—not a guessing game with units.
Drag or use arrow keys to orbit · click the canvas before scrolling to zoom · piston height scales with volume, not vessel dimensions.
0% is the initial state; 100% is the final state. This fraction is not time.
Results will appear here.
Pressure × volume
Single-state mode plots one point. Compare mode plots 101 equilibrium states along the selected constraint. Axes start at zero.
| Path | P (kPa absolute) | V (L) | n (mol) | T (K) |
|---|
Nothing hidden in the units
An ideal gas links its absolute pressure P, volume V, amount n and kelvin temperature T. Three known values determine the fourth.
PV = nRT
R = 8.31446261815324 J mol⁻¹ K⁻¹
At 298.15 K, 1 mol occupying 24.465403697 L gives approximately 101.325 kPa. This is a mathematical state, not a measured gas sample.
Both presets use 273.15 K and 1 mol. At 100 kPa the ideal volume is 22.710955 L. At 1 atm (101.325 kPa) it is 22.413970 L.
1 atm = 101325 Pa
1 bar = 100000 Pa
1 L = 0.001 m³
Do not silently mix the two standard-pressure conventions. Choose the condition your problem specifies.
Compare mode keeps n constant. Halve V at constant T and P doubles. Double V at constant P and kelvin T doubles. At constant V, P changes in proportion to kelvin T.
Isothermal: P₁V₁ = P₂V₂
Isobaric: V₁/T₁ = V₂/T₂
Isochoric: P₁/T₁ = P₂/T₂
These paths are equilibrium comparisons. The tool does not compute heat, work, transition time or piston forces.
No. The ideal-gas approximation ignores particle volume and interactions. Real gases can depart from it, especially near condensation or at high densities. The calculator does not identify gas species, apply an equation of state or certify validity. Never use it as pressure-vessel design or gas-handling guidance.
Software limits in SI units: pressure 10⁻⁶–10⁹ Pa; volume 10⁻¹²–10⁶ m³; amount 10⁻¹²–10⁹ mol; temperature 0.001–100,000 K. Inputs and solved values must stay within these ranges. Zero or negative absolute pressure, volume and amount are invalid; temperature must remain strictly above absolute zero. These are numerical limits, not real-gas operating limits. Decimal or scientific notation is accepted; use a dot for decimals. No uncertainty propagation is performed.
The piston height shows volume relative to the larger endpoint. For extreme ratios, the smaller chamber can appear as a very thin layer. The cylinder is not a dimensioned design. Its 48 markers do not represent molecule counts, measured speeds or physical collisions. Animation is off by default and is silent.
JSON includes current known inputs with their original units, the solved state, selected path, final state, inspected fraction and 101 SI path samples (one in single-state mode). CSV includes the same sample values, current inputs and selected fraction. The solved input is blank in CSV and null in JSON because it was not supplied as known data. Calculations and files stay in this browser; this tool does not save your settings.
Equation and path conventions: OpenStax Chemistry 2e, §9.2. Constant: NIST molar gas constant. Exact defining constants: BIPM kelvin and BIPM mole. R = NAkB; arithmetic uses JavaScript double precision. Graphics and examples here are original schematic illustrations, not copied textbook figures.
Maintained by FastTool · Method prepared October 14, 2026 · Report an issue