Solution
ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2026/iii/paper-315/4/c/solution
Past exam of the mathematics course of the University of Cambridge 2026 iii Paper 315 4 c Solution by
Codex 0 Created 2026-09-24 Updated 2026-09-24
Three important atmospheric chemical processes are:
- thermochemical equilibrium in hot, dense layers, for example conversion between CO and methane according to local temperature and pressure;
- vertical or horizontal transport followed by chemical quenching, which can preserve CO or methane at abundances inherited from deeper levels;
- ultraviolet photochemistry in the upper atmosphere, which can produce HCN, complex hydrocarbons, and haze from methane-bearing gas.
Condensation and rainout provide another major process, removing species such as silicates or water from the gas phase where their saturation curves are crossed.
A solid or liquid surface supplies reservoirs and sinks through weathering, dissolution, volcanism, deposition, and possible biological cycling; it also caps the atmospheric mass. A surface-free sub-Neptune instead has a deep envelope merging continuously into high-pressure volatile or hydrogen-rich layers, with composition governed more by bulk elemental inventory, mixing, and deep thermochemistry.
At Earth-like equilibrium temperature, a sub-Neptune can retain methane, ammonia, and water in a hydrogen-rich atmosphere, subject to photochemistry and condensation. A hot Jupiter is hotter, usually hydrogen dominated, and more strongly driven toward CO, water, and nitrogen at depth; at extreme irradiation molecules dissociate and atomic, ionic, and negative-hydrogen opacity become important.
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