Ideal Gas Laws Back EN | ZH
Thermodynamics Tool

Ideal Gas Law Calculator & PV Diagram

Solve $PV = nRT$ for any variable. Visualize isothermal, isobaric, isochoric, and adiabatic processes on a live P-V diagram.

Solve for
Unit: Pa (1 atm = 101325 Pa, 1 kPa = 1000 Pa)
Unit: m³ (1 L = 0.001 m³)
Unit: K (T = °C + 273.15)
Unit: mol
← Select a variable and calculate
Process Settings
Monatomic: 1.667 / Diatomic (air): 1.4 / Polyatomic: 1.3
Pressure P [kPa]
Volume V [L]
Temperature T [K]
Work W [J]

Theory

Ideal Gas Law:

$$PV = nRT \quad (R = 8.314\ \text{J/(mol·K)})$$

Process relations and work done:

Isothermal: $PV = \text{const}$,  $W = nRT\ln\!\dfrac{V_2}{V_1}$

Isobaric: $\dfrac{V}{T} = \text{const}$,  $W = P\Delta V = nR\Delta T$

Isochoric: $\dfrac{P}{T} = \text{const}$,  $W = 0$

Adiabatic: $PV^\gamma = \text{const}$,  $W = \dfrac{P_1V_1 - P_2V_2}{\gamma - 1}$

CAE Applications: Ideal gas boundary/initial conditions for CFD (FLUENT/OpenFOAM) / Adiabatic process validation in compressible flow simulations / Thermodynamic cycle (Brayton, Carnot) state point calculations / Reference state setup for thermal expansion in ANSYS Mechanical.