Enter Gas and Process Data
The calculator assumes ideal-gas behavior and constant heat capacities over the selected temperature range.
Entropy Change Plot
This graph shows cumulative entropy change from the initial state to the final state.
Example Data Table
Sample values below use air, 2 mol, a general ideal-gas path, and constant heat capacities.
| Gas | n (mol) | T1 (K) | T2 (K) | V1 (m³) | V2 (m³) | Cv (J/mol·K) | ΔS (J/K) |
|---|---|---|---|---|---|---|---|
| Air | 2.00 | 300 | 450 | 0.050 | 0.090 | 20.79 | 26.62 |
Formula Used
General ideal gas change using temperature and volume
ΔS = nCᵥ ln(T₂/T₁) + nR ln(V₂/V₁)
General ideal gas change using temperature and pressure
ΔS = nCₚ ln(T₂/T₁) − nR ln(P₂/P₁)
Isothermal path
ΔS = nR ln(V₂/V₁) = −nR ln(P₂/P₁)
Isobaric path
ΔS = nCₚ ln(T₂/T₁)
Isochoric path
ΔS = nCᵥ ln(T₂/T₁)
Reversible adiabatic path
ΔS = 0
Here, n is moles, R is the universal gas constant, Cₚ and Cᵥ are molar heat capacities, and all absolute temperatures must be in kelvin.
How to Use This Calculator
- Select the process model that best matches your gas path.
- Choose a preset gas or enter custom heat capacities.
- Pick whether you want to calculate from moles or from mass.
- Choose input units for temperature, pressure, and volume.
- Enter the initial and final state values you know.
- Optionally enter an initial entropy reference to estimate final entropy.
- Press Calculate Entropy to view the result above the form.
- Use the CSV and PDF buttons to save the result summary.
FAQs
1) What does this calculator measure?
It estimates the entropy change of an ideal gas between two states. It supports general, isothermal, isobaric, isochoric, and reversible adiabatic paths using constant heat-capacity values.
2) Why are temperature ratios used in the formulas?
Entropy relations for ideal gases come from integrating reversible heat transfer terms. That integration naturally produces logarithms of temperature, pressure, and volume ratios rather than simple differences.
3) Can I use Celsius inputs?
Yes. The form accepts Celsius or kelvin. Internally, the calculator converts values to kelvin before applying the entropy equations because absolute temperature is required.
4) What if I only know pressure values?
For isothermal mode, pressure ratios are enough. For the general mode, you also need T1 and T2. If enough state data is present, the calculator can derive a missing pressure or volume using the ideal gas law.
5) Why does the calculator warn about Cp and Cv?
For an ideal gas, Cp − Cv should be close to the universal gas constant. A warning appears when custom values differ noticeably, because that may indicate inconsistent inputs or non-ideal assumptions.
6) When is the entropy change exactly zero?
A reversible adiabatic process has zero entropy change for the gas. Irreversible adiabatic processes can still generate entropy, but that case is not the same as the reversible model used here.
7) Is this suitable for real-gas accuracy?
It is best for ideal-gas or near-ideal conditions. For high pressures, phase change regions, or strongly temperature-dependent properties, use a real-gas model or tabulated thermodynamic data.
8) What do the CSV and PDF buttons export?
They export the computed summary table, including process type, gas data, state values, heat capacities, and final entropy results. This helps with reporting, lab records, and engineering documentation.