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Energy transport by bulk fluid motion together with local thermal conduction. A prescribed adiabatic process profile constrains temperature but does not require zero convergence of this energy transport. A cloud held at a specified temperature can therefore have nonzero net radiative heating balanced by convection.

A uniform-density perfect-gas sphere supported by decreasing pressure has buoyancy frequency squared $N^2=-2{\omega }_d^2{r}^2/[\gamma (R^2-r^2)]$ in the interior. Its specific entropy decreases outward and adiabatic displacements are buoyantly unstable. For the nonradial polynomial family, the product of the two normalized squared mode frequencies is $-l(l+1)$, displaying one growing branch even when radial compression modes are stable.

A constant radiative-diffusion coefficient and constant gravity give $T^4=T_0^4+4AP/g$. Thus ${\nabla }_{\mathrm{rad}}=AP/(g{T}^4)<1/4$ for $T_0>0$. A diatomic ideal gas has adiabatic temperature gradient $2/7$, so this idealized profile never becomes convective. A physical radiative-convective boundary requires additional opacity, flux, or thermodynamic variation.

Photoionization changes the ion population, often removing bound-state coolants at temperatures where collisional equilibrium would retain them. It can therefore suppress primordial line-cooling peaks. It also supplies photoionization heating. The net loss is cooling minus heating and depends on radiation spectrum, intensity, shielding and gas density. A universal density-independent function of temperature alone is not generally sufficient for irradiated gas.

Equating the optically thin cooling time to the uniform-sphere free-fall time gives a critical gas density proportional to $T^2/{\Lambda }^2$. With hydrogen mass fraction $X$, particle ratio $\chi$ and gravitating gas fraction $f_g$, it is $[32G{m}_p/(3\pi X{f}_g)][3\chi k_{B}T/(2\Lambda ){]}^2$. At fixed temperature, gas above this density cools faster than free fall. A smaller gravitating gas fraction moves the boundary upward because gravity is faster at a fixed gas density.

Two added electrons move above a frozen filled Fermi sea and attract within a thin energy shell. The Pauli-blocked continuum has a logarithmic pair susceptibility, so an arbitrarily weak net attractive constant interaction produces a state below the two-particle threshold at zero temperature. This two-added-particle result is not by itself a full many-electron superconducting state.

A semiconductor used in the exciton absorption experiment in copper(I) oxide.

Core body temperature refers to internal temperature, distinguished from skin temperature. Different measurement sites are proxies with their own limitations, not interchangeable readings of a perfectly uniform interior. ^[ref]

The interface between Earth's metallic core and silicate mantle, approximately 2890 km beneath the surface. It is a major material interface and a thermal boundary across which core heat enters the mantle. Its temperature is distinct from mantle potential temperature because pressure and the lower thermal boundary layer matter.

When an energy Hamiltonian contains $-h{\sum }_n{\sigma }_n$, differentiating its partition function gives $\chi =({\beta }_{\mathrm{th}}/N)\mathrm{Var}({\sum }_n{\sigma }_n)$. Translation invariance converts this to the connected-correlation sum. A dimensionless source ${\beta }_{\mathrm{th}}h$ removes the explicit inverse-temperature factor. In continuum physical coordinates the lattice sum includes the site-density factor $a^{-D}$. A selected pure thermodynamic phase is needed below an ordered transition to avoid a macroscopic mixture contribution.

The Cosmic Background Explorer connected two questions: does the cosmic microwave background follow a Planck spectrum, and how does its temperature vary across the sky? John C. Mather and George F. Smoot shared the 2006 Nobel Prize in Physics for these discoveries.^[ref] The FIRAS and COBE DMR comparisons below explain why measuring spectral shape and measuring angular structure require different information.

Cosmic microwave background anisotropies are direction-dependent perturbations of the relic radiation temperature and polarization.

The cosmic microwave background temperature is about $2.725\mathrm{K}$, corresponding to the displayed thermal energy. The conversion uses $k_B\simeq 8.61733\times 10^{-5}eV/K$. Thus $2.35\mathrm{meV}$ would correspond to about $27.3\mathrm{K}$, rather than the present CMB. Primary references are NASA's CMB temperature measurements and NIST's Boltzmann constant in electronvolts per kelvin.

The cosmic neutrino background is the relic population of neutrinos that thermally decoupled before electron-positron annihilation. Entropy transfer to photons gives

For an adiabatically expanding homogeneous universe, the entropy density satisfiesso the entropy $s{a}^3$ in a comoving volume is constant.

A heat exchanger in which the two streams move in opposite directions. Returning cold helium can cool incoming compressed helium before its expansion in helium liquefaction.

Writing $\mathcal{F}=n_e/n_B$ couples the two equilibrium equations:

Two separately mixed layers with an interfacial thermal bottleneck require separate energy budgets. For lower input $F$, interlayer transfer $J$, surface loss $E$, and per-area heat capacities $H_l,H_u$, these are $H_l{\dot{T}}_l=F-J$ and $H_u{\dot{T}}_u=J-E$. At equilibrium all three fluxes agree, but a finite interface resistance retains a temperature difference. Thus layer count alone does not specify the cooling rate.

Confining a near-critical fluctuating order parameter changes its free energy. Its range is governed by the growing correlation length, and its sign depends on the boundary preferences. This is a thermal collective effect, distinct from the zero-temperature ideal-conductor electromagnetic formula.

The critical micelle concentration is the approximate surfactant concentration above which additional dissolved amphiphile predominantly enters micelles rather than remaining as isolated molecules. It is a concentration crossover governed by equality of the molecular chemical potential in the two environments, not a claim that absolutely no aggregates exist below a sharp threshold. Temperature, ionic conditions and molecular structure affect its value.