A simple gas model relates pressure, amount, volume and temperature.
Key knowledge
An ideal gas obeys pV = nRT. For real gases it is an approximation whose quality depends on density, temperature and interactions; T is absolute thermodynamic temperature.
Values and equations
pV = nRT
p
Absolute gas pressure Pa
V
Gas volume m³
n
Amount of gas mol
R
Molar gas constant J mol⁻¹ K⁻¹
T
Absolute thermodynamic temperature K
Conditions and scope
Use absolute pressure and temperature in kelvins.
The gas is described by a uniform equilibrium state; dense gases and conditions near condensation can depart substantially from the model.
Sources · 3
References
Sources retain their recorded scope. A source link alone does not establish verification of every statement.
OpenStax 2.1, ideal molecular model and gas law; NASA pV = nRT and absolute-temperature restriction.
2026-10-10 · Ideal-gas equation and approximation limits only; no numerical R or real-gas correction is introduced.
Foundational review
2026-10-10 · Fresh primary-source inspection of the complete compact record, including every statement, equation, quantity and material condition, followed by independent AI editorial review. This check does not certify all linked lessons or every passage of every cited publication.
Sources from other places
Agreement within this scope
The dilute ideal-gas equilibrium model relates absolute pressure, volume, amount and temperature by pV=nRT.
Real gases approach this model under suitable dilute conditions; it is not an exact equation for every gas.
National Council of Educational Research and Training (NCERT)
In a nondegenerate ideal ionized mixture in local thermal equilibrium, ions and electrons contribute their number densities to gas pressure; isotropic thermal radiation adds a radiation-pressure term. P=(nᵢ+nₑ)k_BT+a_RT⁴/3. Ionization and composition determine particle numbers; different electron and ion mean masses must not be conflated.
Separate classical particles supply ideal pressure.
For a dry ideal-gas atmosphere in hydrostatic/geostrophic balance, pressure-coordinate shear satisfies ∂u_g/∂p=R_d T_y/(fp) and ∂v_g/∂p=−R_d T_x/(fp). Horizontal temperature gradients here are on constant-pressure surfaces. Integrating between two pressure levels gives their geostrophic wind difference; it does not set the wind at either level by itself.
The specific dry-air ideal-gas relation closes the pressure conversion.
The Boltzmann equation evolves a dilute one-particle distribution with streaming, force and collision terms. Closing the two-particle distribution by uncorrelated incoming velocities, together with binary short-duration collisions, yields a kinetic approximation. Detailed-balance equilibrium and an H theorem depend on those assumptions; they do not prove irreversible equilibration for every microscopic many-body state.
The dilute equilibrium ideal gas is a limit of the kinetic description.
For a mechanically quasistatic simple compressible closed system, work done by the system is W=∫p dV: expansion contributes positive work and compression negative work. A quasistatic isothermal ideal gas with fixed amount gives W=nRTln(V_f/V_i). Isochoric means constant volume; isobaric constant pressure; isothermal constant temperature; adiabatic means no heat transfer.
The two records describe related physical or metrological models or distinctions; the present claim does not require every hypothesis or result in the linked record.
A fixed amount of calorically ideal gas undergoing a reversible adiabatic process obeys pV^γ=constant and TV^(γ−1)=constant, with γ=C_p/C_V>1. The gas cools during such expansion and warms during compression. An insulated free expansion has Q=W=0 and unchanged ideal-gas internal energy; it does not follow this reversible power law.
This relation concerns the stated reversible adiabatic ideal-gas relations claim and its conditions; it does not assert an unqualified prerequisite or an additional theorem.
For a dilute classical ideal gas with isotropic molecular velocities in its rest frame, elastic wall collisions transfer momentum and give pV=Nm⟨v²⟩/3. Combining this with pV=Nk_BT gives mean translational kinetic energy m⟨v²⟩/2=3k_BT/2 and rms speed √⟨v²⟩=√(3k_BT/m). The rms speed is distinct from the mean speed and the net drift velocity.
The molecular count form pV=Nk_BT is the existing amount-of-substance ideal-gas relation with n=N/N_A and R=N_Ak_B.