ONE FORMULA, ONE ANSWER
Ideal gas mixing entropy calculator
Find the entropy increase when distinct ideal gases, initially separated at the same temperature and pressure, are mixed. Choose input units and calculate one value within the stated conditions.
Inputs
Calculations run in this browser. Scientific notation such as 1.2e-3 is supported. Do not group thousands.
Result
Entropy increase on mixing ΔS
Enter values and select Calculate.
ΔSmix = −R Σ[nᵢ ln(xᵢ)]; xᵢ = nᵢ/Σnᵢ; lim(nᵢ→0⁺) nᵢ ln(nᵢ/Σnⱼ) = 0
Assumptions
Each row represents one distinct chemical species. Combine amounts of the same gas into one row. Required: equal initial temperature and pressure for all gases. Excluded: reaction, phase change and nonideal behavior. Zero-amount rows are ignored and at least one row must have positive amount. With only one gas species the mixing entropy is zero.
Displayed values are floating-point approximations. Design safety factors and unprovided error contributions are not calculated.
Formula references and credits
NaNa Lab created the code, descriptions, icons and preview images. Text, figures and code from the linked references have not been reproduced.
Physical constants: NIST / CODATA 2022. The values of μ₀ and ε₀ are measured recommendations, not exact defining constants. Values and precision notes are in the source record.
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