PhysSandbox
Classical MechanicsWaves & SoundElectricity & MagnetismOptics & LightGravity & OrbitsLabs
🌙Astronomy & The Sky🌡️Thermodynamics🌍Biophysics, Fluids & Geoscience📐Math Visualization🔧Engineering🧪Chemistry

More from Thermodynamics

Other simulators in this category — or see all 31.

View category →
NewSchool

Stirling Cycle

PV: two isotherms and two isochores; ideal η equals Carnot with a perfect regenerator.

Launch Simulator
NewSchool

Wet Steam (T–s sketch)

Vapor dome, horizontal isobar in two-phase region, quality x and superheat sketch.

Launch Simulator
NewSchool

Brayton Cycle (Gas Turbine)

PV: isentropic compress, isobaric heat in, isentropic expand, isobaric cool — jet/GT core cartoon.

Launch Simulator
NewSchool

Joule–Thomson Throttling

Isenthalpic expansion: ideal gas ΔT = 0; toy μ_JT inversion for real gases.

Launch Simulator
NewUniversity / research

van der Waals Isotherms

Reduced (P_r,V_r,T_r) curves; critical point; subcritical wiggle vs Maxwell plateaus (qualitative).

Launch Simulator
NewSchool

Bénard Convection (Rayleigh)

Heated-from-below layer: Ra vs Ra_c ~1708; schematic hex/roll pattern.

Launch Simulator
PhysSandbox

Interactive physics, chemistry, and engineering simulators for students, teachers, and curious minds.

Physics

  • Classical Mechanics
  • Waves & Sound
  • Electricity & Magnetism

Science

  • Optics & Light
  • Gravity & Orbits
  • Astronomy & The Sky

More

  • Thermodynamics
  • Biophysics, Fluids & Geoscience
  • Math Visualization
  • Engineering
  • Chemistry

© 2026 PhysSandbox. Free interactive science simulators.

PrivacyTermsContact
Home/Thermodynamics/Gas Mixing & Entropy

Gas Mixing & Entropy

Imagine two distinct gases, such as nitrogen and oxygen, initially separated by a partition within a rigid, insulated container. Each gas occupies an equal volume and contains an equal number of moles. This simulator visualizes the fundamental thermodynamic process of mixing when the partition is removed. The core physics principle at play is the increase in entropy, a measure of molecular disorder or the number of microscopic configurations available to the system. For ideal gases at constant temperature, the entropy change of mixing is derived from the statistical (Boltzmann) definition, S = k_B ln W, where W is the number of microstates. Upon removal of the partition, each gas expands isothermally into the total volume, doubling its available space. The entropy increase for one species is nR ln(V_final/V_initial) = nR ln 2. Since the process is independent and identical for both gases, the total entropy change is ΔS_mix = 2nR ln 2. The simulator makes key simplifications: it treats gases as ideal, assumes no intermolecular forces, neglects any thermal effects (isothermal condition), and considers the container walls to be adiabatic and rigid. By interacting with the simulation, students can directly observe the irreversible mixing process, connect the macroscopic event to the statistical molecular picture, and verify the quantitative prediction for entropy change. It reinforces the Second Law of Thermodynamics and provides a clear, calculable example of entropy generation in a closed system.

Who it's for: Undergraduate students in physics, chemistry, or engineering taking a first course in thermodynamics or statistical mechanics.

Key terms

  • Entropy
  • Ideal Gas
  • Second Law of Thermodynamics
  • Isothermal Process
  • Statistical Mechanics
  • Gibbs Paradox
  • Irreversible Process
  • Mixing

Partition

Two ideal gases A and B, equal moles, same temperature and pressure, each in volume V. Removing the wall doubles the accessible volume for each species. For distinguishable gases, ΔS = n_A R ln 2 + n_B R ln 2.

Shortcuts

  • •Remove the partition to let species mix
  • •Reset restores the wall and separated regions

Measured values

n per species (model)28
ΔS = 2nR ln 238.816
Mixing formula (same value)38.816

How it works

Mixing of distinct ideal gases at constant T increases entropy because each species spreads into twice the volume. Identical particles require quantum Gibbs paradox treatment; here we show the classical distinguishable mixing case.

Key equations

ΔS = n_A R ln(V_f/V_i) + n_B R ln(V_f/V_i) · y_i = n_i / (n_A+n_B)

Frequently asked questions

Why is the entropy change 2nR ln 2 and not zero? Doesn't the pressure equalize, so nothing really changes?
The entropy increase is due to the increased spatial disorder of the molecules, not a pressure change. Initially, each gas molecule is confined to half the container. After mixing, every molecule can be anywhere in the full volume, vastly increasing the number of possible microscopic arrangements (microstates). Even though the final pressure is uniform, the irreversible expansion of each gas into a larger volume generates entropy. A zero entropy change would only occur if the gases were identical, a subtlety known as Gibbs' Paradox.
Is this mixing process reversible? Can we separate the gases without doing work?
No, the mixing depicted is thermodynamically irreversible. To fully separate the mixed gases back into their original pure states, you must perform work (e.g., using a semi-permeable membrane or a diffusion apparatus) and expel heat to the surroundings. This required work is a direct consequence of the entropy increase; reversing the process would require reducing the entropy of the system, which cannot happen spontaneously.
Does the temperature change during mixing in this simulator?
In this specific model, the temperature is assumed constant (isothermal). This is a simplification that isolates the entropy change due purely to the increase in available volume. In a real, adiabatic container with different gas species, there can be a small temperature change upon mixing (the Joule-Thomson effect for non-ideal gases), but for ideal gases with no intermolecular forces, the internal energy and temperature remain constant during free expansion into a vacuum.
What is the real-world significance of entropy of mixing?
The entropy of mixing is a crucial driver in many chemical and physical processes. It explains why gases and liquids spontaneously diffuse, why salts dissolve in water, and is a key factor in determining the equilibrium state of chemical reactions and phase separations. In industrial applications, understanding this entropy is essential for designing separation processes like distillation or gas purification, which must overcome the natural tendency to mix.