= Solution
The pressure axis increases downward in the sketches. Solid red segments indicate efficient <convection>; blue segments indicate mainly <radiative transfer>. The boundaries are nominal examples, since <radiative-convective boundary> pressure depends on <opacity>, gravity and intrinsic flux.
\Image[/past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2016/iii/paper-315-atmosphere-profiles.png]
{title=Qualitative solar-system, irradiated hot-Jupiter and isolated young-giant temperature profiles with radiative-convective boundaries}
For Earth, the convective <troposphere> lies beneath a radiative <stratosphere>, with the transition near $0.1$--$0.2$ bar. The larger solar-system planets likewise have deep convective regions beneath largely radiative upper atmospheres; their tropopause/upper <radiative-convective boundary> is commonly of order $0.1$--$1$ bar. Their temperatures differ greatly from Earth's, and detached radiative layers can occur deeper down.
For an irradiated <hot Jupiter>, absorbed stellar flux maintains a hot, extended, relatively shallow-gradient radiative atmosphere. In models with a weak old-planet intrinsic flux, the deep <radiative-convective boundary> can lie around $10^2$--$10^3$ bar, with a useful wider model-dependent range of tens to thousands of bars. A <thermal inversion> can appear at low pressures if visible/UV absorption heats the upper atmosphere. Below the deep boundary the profile joins a convective adiabat.
A young, <directly imaged exoplanet> on a distant orbit is primarily heated from within. Its <photosphere> commonly joins the convective interior at order $0.1$--$10$ bar, illustrated here at one bar. The temperature generally rises monotonically with pressure over the infrared-forming layers. Strong stellar heating is absent, so a broad stellar-heated isothermal layer is unnecessary.
Two differences in <thermal inversions> are their \b[absorbers and their formation conditions]. Earth's <ozone layer> and solar-system hydrocarbon absorption can heat upper layers; the proposed hot-Jupiter absorbers include refractory <titanium monoxide>/<vanadium monoxide> or other strong visible absorbers, since ozone and <methane>-rich cold-planet chemistry are unsuitable at very high temperatures. Hot-Jupiter inversions depend strongly on irradiation, <atmospheric cold traps> and atmospheric transport, and can occur at mbar-to-sub-bar pressures; Earth and the solar-system giants have cooler, established <stratospheres> above their shallow tropospheres.
Two differences between the <hot Jupiter> and distant young-giant profiles are \b[external versus internal heating, and the depth/shape of the radiative zone]. The former can have a broad warm radiative layer, a much deeper convective boundary and sometimes an inversion; the latter typically has a steeper outward decrease toward a <photosphere>, a shallower boundary and no irradiation-driven inversion. These are class trends, not a unique temperature profile for every planet.
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