What formula does this calculator use?

ΔS = nCv·ln(T₂/T₁) + nR·ln(V₂/V₁), where n is moles, Cv is molar heat capacity at constant volume, R = 8.314 J/(mol·K), and T and V are absolute temperature (Kelvin) and volume. This applies to any process for an ideal gas.

Why must temperature be in Kelvin?

The formula uses a ratio of temperatures (T₂/T₁) inside a logarithm. Ratios only work correctly with an absolute temperature scale. Converting Celsius or Fahrenheit to Kelvin first ensures the math is physically meaningful.

What is Cv for common gases?

Monatomic gases (He, Ar, Ne): Cv = 3R/2 ≈ 12.47 J/(mol·K). Diatomic gases (N₂, O₂, H₂, air) at room temperature: Cv = 5R/2 ≈ 20.79 J/(mol·K). Linear polyatomic gases (CO₂): Cv ≈ 5R/2 to 3R. Non-linear polyatomic (H₂O): Cv = 3R ≈ 24.94 J/(mol·K).

What does a positive ΔS mean?

Positive ΔS means the gas gained entropy — disorder increased. This happens when the gas is heated, expands, or both. A negative ΔS means the gas lost entropy through cooling or compression. The total entropy of the universe (gas + surroundings) must always increase or stay the same for any spontaneous process.

Does this formula work for isothermal or isochoric processes?

Yes. For an isothermal process (T₁ = T₂), the temperature term is zero and ΔS = nR·ln(V₂/V₁). For an isochoric process (V₁ = V₂), the volume term is zero and ΔS = nCv·ln(T₂/T₁). The general formula covers all cases.

Is entropy a state function or path function?

Entropy is a state function — its change depends only on the initial and final states, not the path taken. This is why the same ΔS = nCv·ln(T₂/T₁) + nR·ln(V₂/V₁) formula applies whether the gas was heated at constant volume then expanded isothermally, or taken through any other two-step route.

Entropy of Gas Calculator

Name: Entropy of Gas Calculator
Availability: InStock
Author: Nham Vu

Enter initial and final temperature and volume for an ideal gas to calculate its entropy change (ΔS) using the full thermodynamic formula.

Gas Parameters

Amount of Gas (n) mol

Gas Type (sets Cv)

Molar Heat Capacity at Constant Volume (Cv) J/(mol·K)

T₁ K

T₂ K

Kelvin only. Add 273.15 to convert from Celsius.

V₁ L

V₂ L

Fill in all fields on the left to compute ΔS.

Summary

Enter initial and final temperature and volume for an ideal gas to calculate its entropy change (ΔS) using the full thermodynamic formula.

How it works

Enter the number of moles (n) of gas.
Select a gas type to auto-fill the molar heat capacity Cv, or enter a custom value.
Enter the initial temperature T₁ and final temperature T₂ in Kelvin.
Enter the initial volume V₁ and final volume V₂ in liters.
The calculator applies ΔS = nCv·ln(T₂/T₁) + nR·ln(V₂/V₁) and shows each term separately.
Results display in J/K and J/(mol·K) with a sign interpretation.

Use cases

Thermodynamics coursework on the second law and state functions.
Checking hand calculations for entropy changes in gas processes.
Comparing entropy contributions from temperature vs. volume changes.
Verifying that an isothermal expansion produces positive entropy change.
Analyzing entropy change in gas turbine or compressor stages.
Teaching that entropy is path-independent for ideal gases.
Exploring how monatomic vs. diatomic Cv values affect ΔS.

Frequently Asked Questions

Last updated: 2026-06-10 · Reviewed by Nham Vu