Thermodynamics
Adiabatic Process
Relationship for adiabatic (no heat transfer) process. Also: T₁V₁^(γ-1) = T₂V₂^(γ-1).
Variables
PPa
Pressure
Gas pressure
In SI units: kg/(m·s²)
Vm³
Volume
Gas volume
γunitless
Heat capacity ratio
C_p/C_v (1.4 for diatomic)
Derivation
From first law with Q=0: dU = -PdV. Using PV = nRT and U = nC_vT, derive PV^γ = constant.
Your notes
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Other thermodynamics formulas with the same quantities
- Enthalpy (First Law) shares Pressure, Volume
- Ideal Gas Law (Molecular) (Kinetic Theory) shares Pressure, Volume
- Pressure (Kinetic Theory) (Kinetic Theory) shares Pressure, Volume
- Work Done by Gas (First Law) shares Pressure
- Mean Free Path (Kinetic Theory) shares Pressure
Where this formula is listed
- Thermodynamics formulas, under First Law, alongside Work (Isothermal Process), Internal Energy (Ideal Gas) and Heat Capacity Relation.
- In the thermodynamics list it comes after Internal Energy (Ideal Gas) and before Heat Capacity Relation.
- Thermodynamics formula sheet, one of 34 formulas printed with symbol keys and SI units.
- The full formula index, grouped by category and topic.
Common questions
What is the Adiabatic Process formula?
Adiabatic Process is written PV^γ = constant. Relationship for adiabatic (no heat transfer) process. Also: T₁V₁^(γ-1) = T₂V₂^(γ-1). It belongs to Thermodynamics, under First Law.
What are the units in PV^γ = constant?
In SI units, P is pressure, measured in kg/(m·s²); V is volume, measured in m³; γ is heat capacity ratio (dimensionless).
How is the Adiabatic Process formula derived?
From first law with Q=0: dU = -PdV. Using PV = nRT and U = nC_vT, derive PV^γ = constant. The result is PV^γ = constant.