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Past exam of the mathematics course of the University of Cambridge 2016 iii Paper 315 4 j Solution Created 2026-10-03 Updated 2026-10-06
Three solar-system effects illustrate chemical disequilibrium. First, vertical mixing carries carbon monoxide from hot deep regions into cooler observable layers of giant planets, where its local-equilibrium abundance would be small. Second, phosphine survives in the observable atmospheres of Jupiter and Saturn because deep supply competes with its destruction, making it a tracer of transport. Third, methane photolysis creates hydrocarbons such as ethane and acetylene, and can help form upper-atmospheric atmospheric hazes in giant planets and Titan.
Three exoplanet effects are complementary. First, carbon monoxide–methane quenching can keep carbon monoxide abundant and methane depleted in cool observable gas, including hot-Neptune/giant atmospheres that would locally favor methane. Second, atmospheric photochemistry dissociates methane/ammonia and produces radicals, hydrogen cyanide, hydrocarbons and possibly atmospheric hazes, changing spectral bands from their equilibrium strengths. Third, horizontal chemical quenching can preserve hot-dayside carbon chemistry on the cooler nightside/terminator and reduce the abundance contrast expected from separate local-equilibrium columns.
Transport, photon-driven reactions and finite chemical adjustment times change the observable composition. The effects are conditional on the species' chemical timescale relative to mixing, advection and irradiation; they do not imply that every molecule is out of equilibrium everywhere.
Past exam of the mathematics course of the University of Cambridge 2017 iii Paper 315 4 f Solution Created 2026-10-03 Updated 2026-10-06
Three routes away from local thermochemical equilibrium are:
- Vertical transport and quenching. When the eddy mixing time becomes shorter than the chemical relaxation time, gas retains a deeper composition. In cool, directly imaged giant exoplanets, carbon monoxide–methane quenching can preserve CO and suppress the methane expected in cool equilibrium layers. In Jupiter, CO carried from deeper hot layers, and phosphine maintained against upper-atmosphere chemical loss, are examples of transported disequilibrium species.
- Horizontal transport and quenching. Atmospheric advection time shorter than the local chemical relaxation time carries abundances between regions of different temperature. A hot Jupiter can carry CO-rich dayside gas into cooler nightside gas that would otherwise favour methane. In the Solar System, upper-atmosphere CO produced on the illuminated side of Venus can be redistributed to its dark side by circulation; this is an example of nonlocal production and transport, rather than local dark-side thermochemical equilibrium.
- Atmospheric photochemistry. Ultraviolet photons dissociate or ionize molecules and initiate reaction networks. Models of irradiated hydrogen-rich exoplanet atmospheres can produce enhanced hydrogen cyanide and hydrocarbon precursors from methane/nitrogen chemistry; whether these products accumulate depends on ultraviolet flux and transport. The terrestrial atmosphere gives a clear Solar-System example: oxygen photodissociation and subsequent reactions maintain the ozone layer, which is not a purely thermochemical-equilibrium abundance.
Vertical mixing, horizontal advection, and photochemistry supply three mechanisms and examples in both exoplanets and Solar-System atmospheres. A photochemical steady state balances production and loss; it is different from a Gibbs free energy minimum. These examples describe mechanisms and model expectations rather than asserting unique observational attribution for every planet.