Adiabatic Process Calculator

In an adiabatic process, no heat is exchanged with the surroundings. All work done changes the internal energy, causing temperature to change. Fast compression/expansion in engines approximates this.

🔥 Thermodynamics📐 PVγ = const⚙️ Gas Dynamics
Initial Pressure P₁ (Pa)
Initial Volume V₁ (m³)
Final Volume V₂ (m³)
Gamma γ
Initial Temperature T₁ (K)
Please enter valid values.

Formula & Reference

VariableSymbolFormulaUnits
Adiabatic Relation—P1V1γ = P2V2γPa·m³⊃γ
Temperature Relation—T2 = T1(V1/V2)γ−1K
Gammaγ1.4 for air, 5/3 for monatomic gas—
Adiabatic WorkWW = (P1V1 − P2V2)/(γ−1)J

Step-by-Step Examples

Example 1
Engine Compression

Air at P1=101325 Pa, V1=0.001 m³ compressed to V2=0.0001 m³. Gamma=1.4.

  • P2 = P1(V1/V2)γ = 101325 × 10¹·⁴ = 2,541 kPa
  • T2 = T1 × (V1/V2)γ⁻¹ = 293 × 10°·⁴ = 736 K
✓ 2541 kPa, 463°C — explains diesel ignition
Example 2
Adiabatic Expansion

Gas at 500 kPa, V1=0.002 m³ expands to V2=0.01 m³. Gamma=1.4.

  • P2 = 500,000 × (0.002/0.01)¹·⁴ = 26,390 Pa
  • T2/T1 = (0.002/0.01)γ⁻¹ = 0.2°·⁴ = 0.381
  • T2 = 293 × 0.381 = 112 K
✓ P2 = 26.4 kPa, T2 = 112 K (-161°C)
Example 3
Work Done in Compression

P1=101325 Pa, V1=1 L, V2=0.1 L, gamma=1.4, T1=300 K.

  • P2 = 2541 kPa
  • W = (101325×0.001 - 2541000×0.0001)/(1.4-1)
  • W = (101.3 - 254.1)/0.4 = -382 J
✓ 382 J of work done ON the gas

Real-World Applications

🚗
Diesel Engines
Diesel ignition occurs because adiabatic compression raises air temperature above diesel fuel flash point (~250°C).
⛅
Atmospheric Physics
Rising air expands adiabatically, cooling at 9.8°C per km (dry adiabatic lapse rate).
💨
Sound Propagation
Sound is an adiabatic process (too fast for heat exchange). Gamma appears in speed of sound formula.
🚀
Rocket Nozzles
Isentropic (reversible adiabatic) flow in rocket nozzles converts heat to kinetic energy.

Common Mistakes to Avoid

⚠️
Using Celsius instead of Kelvin

Temperature relation T2 = T1*(V1/V2)^(gamma-1) requires absolute temperature in Kelvin.

⚠️
Confusing adiabatic with isothermal

Adiabatic: no heat exchange, T changes. Isothermal: constant T (slow process). They give different pressure-volume curves.

⚠️
Wrong gamma for gas

Gamma = 1.4 for air/diatomic. Use 5/3 = 1.667 for monatomic (He, Ar). Polyatomic gases ~1.3.

Frequently Asked Questions

What is the difference between adiabatic and isothermal? ▾
Isothermal: T constant, PV = constant (slow). Adiabatic: no heat exchange, PV^gamma = constant (fast). Adiabatic curve is steeper on a PV diagram.
Why do rising air parcels cool? ▾
Ascending air encounters lower pressure and expands adiabatically. All expansion work comes from internal energy, reducing temperature at ~9.8 K/km.
What is the isentropic efficiency? ▾
Real compressors and turbines have losses. Isentropic efficiency = ideal adiabatic work / actual work. Typically 80-95% for modern machines.
Can a process be both adiabatic and reversible? ▾
Yes — this is an isentropic process. Real adiabatic processes are irreversible (entropy increases). Only reversible adiabatic processes satisfy PV^gamma = constant exactly.
Why does diesel ignition not need a spark plug? ▾
Diesel compresses air at ratio ~20:1. Adiabatic compression raises temperature to ~700-900°C, well above diesel autoignition temperature (~250°C).
What is the adiabatic lapse rate? ▾
Dry air cools at 9.8°C/km rising (adiabatically). Moist air cools at ~6°C/km (latent heat of condensation releases energy). Clouds form at the lifting condensation level.
How is adiabatic used in refrigeration? ▾
Throttling through an expansion valve is approximately adiabatic. Pressure drop causes temperature drop (Joule-Thomson effect), cooling the refrigerant.
What is polytropic process? ▾
Generalization: PV^n = constant. n=1 isothermal, n=gamma adiabatic, n=0 isobaric, n=infinity isochoric. Real processes fall between these ideals.

Related Physics Calculators

💨 Ideal Gas Law💨 Specific Heat Ratio⚙️ Carnot Efficiency🌡️ Isothermal Work💨 Gas Pressure

Formula Explorer connections

Interpretation: This formula tracks heat, temperature, work, entropy or transport in a thermodynamic system. Assumption: Use absolute temperature where required and consistent energy units. Constant properties, equilibrium, ideal gases or negligible losses may be assumed.

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