Compute the adiabatic index using thermodynamic measurements quickly. Switch between Cp/Cv, pressure, volume, temperature data. Export results as CSV or PDF for reports today.
γ = Cp / CvP1·V1^γ = P2·V2^γ ⇒ γ = ln(P2/P1) / ln(V1/V2)T·V^(γ−1) = const ⇒ γ = 1 + ln(T2/T1) / ln(V1/V2)T2/T1 = (P2/P1)^((γ−1)/γ) ⇒ γ = ln(P2/P1) / (ln(P2/P1) − ln(T2/T1))γ = 1 + 2/f (ideal gas approximation)Notes: These relations assume an ideal gas and a reversible adiabatic process. Measured states with heat transfer, shocks, or strong real-gas effects can bias γ.
| Scenario | Method | Inputs | Expected γ |
|---|---|---|---|
| Diatomic gas (typical) | Cp/Cv | Cp = 29.1, Cv = 20.8 (J/(mol·K)) | ≈ 1.399 |
| Compression test | P-V | P1 = 101325 Pa, P2 = 180000 Pa, V1 = 0.010 m³, V2 = 0.006 m³ | ≈ 1.344 |
| Expansion with temperature probe | T-V | T1 = 300 K, T2 = 360 K, V1 = 0.006 m³, V2 = 0.010 m³ | ≈ 1.358 |
| Pressure rise with temperature rise | P-T | P1 = 100 kPa, P2 = 220 kPa, T1 = 300 K, T2 = 390 K | ≈ 1.438 |
| Monatomic ideal gas estimate | Degrees of freedom | f = 3 | ≈ 1.667 |
The adiabatic index, γ (gamma), is the ratio of specific heats at constant pressure and constant volume. It controls how strongly a gas resists temperature change during rapid compression or expansion. In many engineering models, γ links pressure, volume, and temperature during an adiabatic process.
For ideal gases, γ depends on molecular structure. Monatomic gases often sit near 1.67, diatomic gases near 1.40, and polyatomic gases commonly range around 1.20–1.33. Lower γ generally means more internal modes store energy, so temperature rises less for the same compression.
When you have reliable heat-capacity data at the same temperature range, γ = Cp/Cv is direct and stable. In laboratory datasets, Cp and Cv may vary with temperature, so the best practice is to use values measured or tabulated close to your operating point and report the reference temperature.
If you record two states during a fast, well-insulated compression, the relation P·Vγ = constant provides γ from logarithmic ratios. Data quality matters: small sensor offsets can distort ln(P2/P1) and ln(V1/V2). Repeating trials and averaging reduces scatter.
Temperature methods are useful when pressure and volume are hard to measure precisely. Because γ uses temperature ratios, use absolute temperature (Kelvin) to avoid offset errors from Celsius or Fahrenheit. The calculator keeps units as labels, but the physics assumes absolute scaling for ratios.
For an ideal gas, γ can be estimated from degrees of freedom using γ = 1 + 2/f. This is a fast sanity check: f = 3 predicts 1.667, f = 5 predicts 1.400, and f = 6 predicts 1.333. Real gases deviate when vibrational modes activate or when non-ideal behavior is significant.
γ affects speed of sound, nozzle flow, compressor outlet temperatures, and shock relations. In internal combustion and gas turbines, choosing γ too high can overpredict temperature rise. In CFD and thermo packages, γ may be treated as constant or temperature-dependent, depending on accuracy needs.
Before exporting, confirm all ratios are positive and that state pairs truly belong to the same process step. If multiple methods disagree, check for heat loss, moisture, sensor lag, or inconsistent units. Report the method, inputs, and computed γ together to make results auditable.
Not always. γ applies to reversible adiabatic behavior of an ideal gas. A polytropic index describes a broader class of processes that may include heat transfer and friction.
Negative or extreme results usually come from invalid ratios in logarithms, swapped state values, or non-adiabatic behavior. Verify P, V, and T are positive and that V1 differs from V2.
Use Kelvin for any method involving temperature ratios. Celsius and Fahrenheit include offsets that can corrupt ratios. If you only have Celsius data, convert to Kelvin before calculating.
Yes, γ can vary with temperature because heat capacities change as molecular modes become active. For high accuracy, use Cp and Cv appropriate to the operating temperature range.
This calculator targets gases where ideal-gas relations are reasonable. Liquids are weakly compressible and require different thermodynamic models; γ is not commonly used the same way.
If you trust Cp and Cv data, use Cp/Cv. Otherwise, use P–V with well-instrumented compression. Temperature-based methods can work, but require careful absolute-temperature handling and timing.
CSV is ideal for spreadsheets and further analysis, while PDF preserves a clean record for reports and sharing. Exporting both keeps your calculations traceable and easy to reuse.
Important Note: All the Calculators listed in this site are for educational purpose only and we do not guarentee the accuracy of results. Please do consult with other sources as well.