Isobaric Process
An isobaric process is a change of state at constant pressure. The work done by the system is W = pΔV, and the heat absorbed equals the enthalpy change, Q = ΔH = nCpΔT for an ideal gas. Volume is then proportional to absolute temperature (Charles's law, V/T = constant).
Curious
Most things that happen in the open air happen at constant pressure: cooking, a balloon warming in the sun, bread dough rising. A hot-air balloon works because air heated at constant pressure expands and becomes less dense (see Ideal Gas Law).
Because some heat is used for expansion work, heating a gas at constant pressure takes more energy than heating it at constant volume; the difference is captured by Cp > Cv (see Specific Heat Capacity) and by enthalpy.
Exploring
| Process | Held constant | Ideal-gas results |
|---|---|---|
| Isothermal | T | Q = W = nRT ln(V2/V1), ΔU = 0 |
| Adiabatic | Q = 0 | pVγ = const, W = −ΔU |
| Isochoric | V | W = 0, Q = ΔU = nCvΔT |
| Isobaric | p | W = pΔV, Q = nCpΔT |
Deep Dive
Thermodynamics. At constant pressure dH = T dS, so Cp = (∂H/∂T)p and ΔS = nCp ln(T2/T1) for an ideal gas. On a p–V diagram an isobar is horizontal, and the work is the rectangular area under it. Isobaric heat addition and rejection appear in the Brayton (gas turbine) and Rankine (steam) cycles (see Heat Engines), and in the boiling and condensing stages of refrigeration cycles.
Phase changes. At constant pressure, a pure substance changing phase stays at constant temperature, so the process is simultaneously isobaric and isothermal, and the heat absorbed equals the latent heat (see Latent Heat). The Gibbs free energy G = H − TS is the natural potential for processes at constant temperature and pressure (see Josiah Willard Gibbs).
History. Jacques Charles observed around 1787 that gases expand by equal fractions for equal temperature rises, but did not publish; Joseph Louis Gay-Lussac published careful measurements in 1802, crediting Charles. The law is often called Charles's law in English-language texts and Gay-Lussac's law in French ones.
Concept Relationship Map
Requires: first law, enthalpy
Enables: Cp, Brayton and Rankine cycles, Gibbs free energy
Commonly confused with: isothermal process
Sources
- Gay-Lussac, J.L. (1802). Annales de Chimie, 43, 137–175.
- Çengel, Y.A., Boles, M.A. (2015). Thermodynamics: An Engineering Approach (8th ed.). McGraw-Hill.
- Schroeder, D.V. (2000). An Introduction to Thermal Physics. Addison-Wesley.