Types of Thermodynamic Processes

Thermodynamics studies how energy moves and transforms within physical systems. At the heart of this field are thermodynamic processes — specific ways a gas (or any system) can change from one state to another. Every time you pump up a bicycle tyre, boil water in a sealed pot, or watch a piston fire in a car engine, a thermodynamic process is taking place. These processes are described by how the key state variables — pressure (P), volume (V), and temperature (T) — change, and which one (if any) is held constant. There are five fundamental process types you must know: isothermal (constant temperature), adiabatic (no heat exchange), isochoric (constant volume), isobaric (constant pressure), and cyclic (the system returns to its original state). Each has a distinct physical interpretation, a signature shape on a Pressure–Volume (P–V) diagram, and a simplified form of the First Law of Thermodynamics. Mastering these five types lets you analyse real engines, refrigerators, and atmospheric phenomena. The First Law of Thermodynamics, ΔU = Q − W, ties everything together: the internal energy change of a system equals the heat added to it minus the work it does on its surroundings. Depending on which constraint is applied, one or more terms simplify to zero, making each process type easier to work with mathematically. Think of it like a budget equation — the constraint tells you which 'account' is frozen.

Key takeaways
  • Isothermal Process (ΔT = 0)
  • Adiabatic Process (Q = 0)
  • Isochoric Process (ΔV = 0)
  • Isobaric Process (ΔP = 0)
  • Cyclic Process (ΔU = 0 over one full cycle)

Isothermal Process (ΔT = 0)

In an isothermal process the temperature of the system stays constant throughout. For an ideal gas, internal energy depends only on temperature, so ΔU = 0. The First Law then gives Q = W: all heat absorbed is converted into work (or vice versa). This requires the process to happen slowly enough for the system to exchange heat with its surroundings — a 'slow leak' of a tyre approximates this. On a P–V diagram, an isothermal process follows a hyperbola described by PV = nRT = constant. The curve is called an isotherm.

Adiabatic Process (Q = 0)

An adiabatic process involves no heat exchange between the system and its surroundings. This can happen because the system is thermally insulated (like gas in a well-insulated cylinder) or because the process is so fast that heat has no time to flow. Since Q = 0, the First Law gives ΔU = −W: any work done by the gas comes entirely at the expense of its internal energy, so the gas cools. Conversely, compressing a gas adiabatically heats it — this is why a bicycle pump gets warm. Adiabats obey PV^γ = constant, where γ = Cp/Cv is the adiabatic index. Adiabats are steeper than isotherms on a P–V diagram.

Isochoric Process (ΔV = 0)

An isochoric (or isovolumetric) process keeps volume constant, so the gas does no work: W = 0. The First Law reduces to ΔU = Q — all heat absorbed goes directly into changing internal energy (and therefore temperature). Heating a rigid sealed container of gas is isochoric. On a P–V diagram it appears as a vertical line: pressure changes but volume stays fixed. The relationship between pressure and temperature is P/T = constant (Gay-Lussac's Law for fixed volume).

Isobaric Process (ΔP = 0)

An isobaric process keeps pressure constant. This is common when a gas expands or contracts in a cylinder with a freely moving piston exposed to atmospheric pressure — the atmosphere acts as a constant-pressure reservoir. Work done is simply W = PΔV. The First Law gives ΔU = Q − PΔV. Heat capacity at constant pressure (Cp) applies here, and Cp > Cv because some of the added heat goes into doing work rather than raising temperature. On a P–V diagram this is a horizontal line.

Cyclic Process (ΔU = 0 over one full cycle)

A cyclic process returns the system to exactly its original state after one complete loop, so the net change in internal energy over one cycle is zero: ΔU_cycle = 0. By the First Law, Q_net = W_net. The net work done equals the area enclosed by the loop on a P–V diagram — clockwise loops represent engines doing positive net work on the surroundings; anticlockwise loops represent refrigerators or heat pumps. Real heat engines such as the Carnot engine and the Otto engine operate on thermodynamic cycles.

The Key Equation

PVγ=constant,γ=CPCVPV^{\gamma} = \text{constant}, \quad \gamma = \frac{C_P}{C_V}
  • P — Pressure (Pa (pascals)): The force per unit area exerted by the gas on the container walls.
  • V — Volume (m³): The space occupied by the gas.
  • \gamma — Adiabatic index (heat capacity ratio) (dimensionless): Ratio of molar heat capacity at constant pressure to that at constant volume. For a diatomic ideal gas (e.g. N₂, O₂) γ ≈ 1.4.
  • C_P — Molar heat capacity at constant pressure (J mol⁻¹ K⁻¹): Heat needed to raise one mole by 1 K at constant pressure.
  • C_V — Molar heat capacity at constant volume (J mol⁻¹ K⁻¹): Heat needed to raise one mole by 1 K at constant volume.

Worked Example

Problem. A monatomic ideal gas (γ = 5/3) at initial pressure P₁ = 3.0 × 10⁵ Pa and volume V₁ = 2.0 × 10⁻³ m³ undergoes an adiabatic expansion to a final volume V₂ = 6.0 × 10⁻³ m³. Find the final pressure P₂.

P2≈4.82×104 PaP_2 \approx 4.82 \times 10^{4} \text{ Pa}

Answer. The final pressure is approximately 4.8 × 10⁴ Pa.

Figure
Diagram
P–V Diagram: Four Thermodynamic ProcessesVPV₁V₂P₁P₂Isochoric(ΔV=0)Isobaric (ΔP=0)Isothermal(ΔT=0)Adiabatic(Q=0)Start (V₁,P₁)IsochoricIsobaricIsothermalAdiabatic
Origins · 1 minSadi Carnot and how this was discovered
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Sadi Carnot
1796–1832 · French

Sadi Carnot founded the science of thermodynamics with his 1824 work 'Reflections on the Motive Power of Fire.' He introduced the concept of the Carnot cycle — a theoretical cyclic process consisting of two isothermal and two adiabatic steps — and proved that no heat engine can be more efficient than this ideal cycle. His work laid the conceptual foundation for the Second Law of Thermodynamics, decades before it was formally stated. Carnot died of cholera at just 36 years old. Most of his unpublished notes were buried with him as a precaution against spreading the disease, meaning much of his advanced thinking about thermodynamics was lost to history.

  • First Law of Thermodynamics — The First Law (ΔU = Q − W) is the governing equation used to analyse every thermodynamic process; each process simplifies it differently.
  • Ideal Gas Law — PV = nRT relates the state variables P, V, and T, underpinning the mathematical description of isothermal, isobaric, and isochoric processes.
  • Carnot Cycle and Engine Efficiency — The Carnot cycle is a specific cyclic process combining adiabatic and isothermal steps, defining the upper limit of heat engine efficiency.
  • Entropy and the Second Law of Thermodynamics — Entropy change in a process depends on its type — entropy is conserved in reversible adiabatic processes but increases in irreversible ones.