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The 1933 report Ein neuer Effekt bei Eintritt der Supraleitfähigkeit by W. Meissner and R. Ochsenfeld describes cooling tin and lead cylinders in a fixed transverse magnetic field. Two parallel cylinders were about $140\mathrm{mm}$ long and $3\mathrm{mm}$ thick, separated by $1.5\mathrm{mm}$. A roughly $10\mathrm{mm}$ rotating search coil between them drove a ballistic galvanometer. At about $5\mathrm{G}$, the reported below/above-transition induction ratios were $1.70$ for tin single crystals and $1.77$ for polycrystalline lead. The increased gap magnetic field indicates redistribution outside the cylinders, rather than an unchanged frozen field. Coil-winding geometry and noncircular tin specimens limited comparison with the ideal prediction. ^[ref]

Their second arrangement used a lead tube, about $130\mathrm{mm}$ long with $3\mathrm{mm}$ outer and $2\mathrm{mm}$ inner diameters. A rotating search coil could sit inside or alongside it. The bore retained magnetic flux after removing the applied magnetic field; the coil nearly filled the bore, preventing a test of interior field uniformity. A hole containing magnetic field is distinct from magnetic field penetrating the surrounding material exhibiting superconductivity. ^[ref]

The modern Field-cooled Meissner experiment provides a complementary readout. MIT's probe I places a sample in a brass holder, with an $810$-turn test coil of $7.1\mathrm{mm}$ inner diameter, $10.5\mathrm{mm}$ outer diameter and $12.3\mathrm{mm}$ length, inside a longer solenoid. A nearby silicon-diode thermometer tracks cooling by helium gas. With lead still normal, the guide applies about $200\mathrm{mA}$ to the solenoid and connects the test coil to a current-integrator box and oscilloscope. Cooling produces a transient; warming gives the opposite sign. Switching off the solenoid while the sample is normal checks the sign. ^[ref]

The inferred change is in linked magnetic flux, not a direct scan of $B(z)$. For a stationary test coil the pulse obeys $\int Vdt=-\Delta \Psi$, where $\Psi$ is its magnetic flux linkage. An integrator or AC-coupled oscilloscope needs its transfer response accounted for before extracting this pulse area. Keep the source electric current fixed during cooling, monitor temperature, and compare warming and cooling slowly enough to reduce sample–thermometer lag. An AC inductance change alone can reflect changed normal-state electrical conductivity; the fixed-field expulsion test distinguishes that alternative. ^[ref] Neither this coil readout nor the historical gap-field measurement resolves the microscopic London penetration depth by itself.

Floating ice with submerged volume fraction $f$ has density $f{\rho }_l$ by Archimedes' principle. Its volume change on melting is therefore $v_l-v_s=(1-1/f)/{\rho }_l<0$. An enthalpy cycle gives $L_f=L_s-L_v$ for quantities consistently expressed per mass at the same temperature. Treating these latent heats and specific volumes as constant and integrating the Clausius-Clapeyron relation gives the displayed pressure estimate. Using a vaporization latent heat extrapolated from a different temperature carries that approximation into the inferred fusion heat.

A membrane osmometer connects osmosis to a visible liquid level or a measured balancing pressure. In a teaching version, a solute-containing pouch is joined to a narrow vertical tube and submerged in external water. Entry increases the enclosed volume and raises the meniscus. Both the column and any stretched pouch can contribute an opposing pressure.

The University of Toronto's Osmosis (Brine) by University of Toronto Department of Physics demonstration (activity Me-012b, Description, steps 1–14) specifies soaking a dialysis membrane tube, tying one end closed and fastening the other around a thistle tube's narrow end. A stand holds the tube. Colored brine is cooled to room temperature and injected using a syringe to reduce bubbles; the pouch is completely immersed in a $1$ or $2\mathrm{L}$ beaker of distilled water. A taped marker records the initial level; subsequent meniscus height is the readout. The protocol proposes another pouch containing distilled water as a comparison, and its older instructions explicitly check seals for leaks.^[ref]

A rise is consistent with net water entry. To infer osmotic pressure quantitatively, use a retained solute and establish a stable equilibrium after accounting for dilution. If both free surfaces are at the same atmospheric pressure, the liquids have approximately equal mass densities $\rho$, and the pouch adds negligible mechanical load, the hydrostatic pressure difference at membrane height is approximately $\Delta P=\rho gh$, where $h$ is the meniscus height above the external surface and $g$ is gravitational acceleration. This is the liquid-column inference, not a pressure calibration supplied by the Toronto demonstration. For unequal mass densities, compare the two column pressures separately.

Useful additional controls are matched initial levels and geometry, constant temperature, replicate runs, and monitoring external solute to test retention. These are proposed checks, not reported Toronto results. Leaks, trapped bubbles, surface tension in the narrow tube, evaporation and membrane stretching can alter the level. In particular, a dialysis membrane may pass dissolved salt: the brine setup illustrates transient movement but cannot be assumed to retain every dissolved ion. Color improves visibility without proving salt retention. A stationary level can reflect weakening concentration differences or leakage rather than osmotic thermodynamic equilibrium; a rising level alone supplies neither $n$ nor a verified value of $nRT/V$.

Membrane transport is the passage of substances across a cell membrane. For the small solutes considered here, distinguish the available route from its driving force: a lipid bilayer, ion channel, or carrier protein determines how passage can occur, while differences in chemical potential and membrane potential determine which direction is energetically downhill. A large driving force cannot make an unavailable route conduct. See Alberts et al.: principles of membrane transport.

For an ideal dilute chemical solution at uniform temperature and pressure, with the same reference molar chemical potential on both sides, the molar electrochemical potential change for transferring a solute from compartment A to B isHere $c_{\mathrm{A}},c_{\mathrm{B}}$ are concentrations, $T$ is absolute temperature, $R$ is the molar gas constant, $z$ is signed ion charge number, $F$ is the Faraday constant, and $V_{\mathrm{B}}-V_{\mathrm{A}}$ is the electric potential difference. The natural logarithm contains a dimensionless ratio. The electrical term vanishes for an uncharged solute. More generally, use thermodynamic activities in place of the ideal concentration ratio. This combines the ideal-solution chemical potential difference with electrical energy per mole; see IUPAC Gold Book: electrochemical potential. For a biological cell, taking B inside and A outside makes the voltage term use the existing membrane potential convention.

The component of heat transport crossing a latitude. A poleward transport is northward in the Northern Hemisphere and southward in the Southern Hemisphere. Equal and opposite volume transports can carry net heat when the poleward branch is warmer. For eddies, the corresponding transport is determined by the correlation of meridional velocity and temperature anomalies, closely related to eddy buoyancy flux in a thermal Boussinesq approximation.

The mesosphere lies above the stratosphere and below the thermosphere. Its typical terrestrial temperature decreases upward.

A change between a material behaving as an electrical conductor and as an electrical insulator. The distinction concerns the limiting electronic response as temperature tends to zero; finite thermally activated electrical conductivity alone does not establish a metallic state. A Peierls transition opens a band gap through a change in the crystal structure.

Heavy elements provide many ionic transitions at temperatures where hydrogen and helium have lost their most effective line emitters. Metal-line cooling can therefore increase the plasma cooling function substantially and broaden its temperature features. Low-energy fine-structure transitions also permit cooling below the hydrogen atomic threshold when the relevant ions and electrons are present.

Epitaxial growth using volatile metal-organic precursors delivered in the gas phase. Precursor decomposition and surface incorporation grow a crystalline compound layer or nanostructure; temperature and mass transport influence composition.

A grouping of mineral assemblages characteristic of a range of temperature and pressure, allowing for the original rock composition.

Rock transformed by changes in temperature, pressure, deformation or fluid conditions while predominantly remaining solid.

Changes in a rock’s mineral assemblage, texture or composition under altered pressure, temperature or fluid conditions, conventionally dominated by solid-state processes.

Statistical analysis of metamorphic temperature/pressure distributions and their secular evolution. Nature 572, 378–381; DOI 10.1038/s41586-019-1462-2.

A meteorologist studies the atmosphere and weather using observations, physical theory and numerical models. Fluid mechanics, thermodynamics and radiative processes connect measured pressure, temperature and moisture with changing winds and clouds.

Forecasting requires an estimated initial state as well as evolution equations. Uncertainty in observations and model approximations can grow, so an ensemble of forecasts is useful for expressing a range of plausible outcomes.

Meteorology studies atmospheric structure, motion and the processes producing weather. Uneven heating generates pressure gradients, air motion transports heat and water vapor, and condensation or freezing releases latent heat. Rotation and surface friction help determine how that motion develops.

A weather station measures local conditions, while comparing observations over space reveals evolving atmospheric systems. Wind, temperature, relative humidity and pressure constrain different parts of the physical state; no one sensor completely describes it. Forecasts combine these observations with equations for fluid motion, energy and moisture. Climatology instead emphasizes statistics over longer periods, using many of the same physical mechanisms and observing systems.

Infer an unknown heat capacity by thermal contact with a calibrated receiver and a measured common final temperature. The energy lost by hotter components equals the energy gained by colder components, with the calorimeter and surrounding heat transfer included. For appreciably varying heat capacities, use temperature integrals rather than constant $mc\Delta T$ terms.

Michael Dopita modeled the physical processes producing emission from ionized astronomical gas. With David C. Nicholls and Ralph S. Sutherland, he investigated why different spectral lines can give discrepant electron temperatures and chemical abundances in H II regions and planetary nebulae.

Their proposed explanation changed the assumed electron kinetic energy distribution from a Maxwell-Boltzmann distribution to a Kappa distribution, which has a more populated high-energy tail. Because different atomic transitions sample different electron energies, this change affects their inferred temperatures differently. The paper presented a testable interpretation of the diagnostic discrepancy.^[ref]

The Michaelis-Menten equation describes a saturating enzyme reaction rate:Here $s$ is free substrate concentration, $V_{\max }$ is the limiting rate at large $s$, and the Michaelis constant $K_M$ is the concentration giving $v=V_{\max }/2$.

For the elementary mechanism $E+S\rightleftharpoons ES\to E+P$, use binding rate constant $k_1$, dissociation rate constant $k_{-1}$ and turnover number $k_{\mathrm{cat}}$. The quasi-steady-state approximation sets the fast enzyme-substrate complex balance towhere $e_T$ is total enzyme concentration and $c=[ES]$. Solving givesThis modern steady-state derivation does not require substrate binding to be in chemical equilibrium. In particular, $K_M$ is not generally the binding dissociation constant.

At $s\ll K_M$, $v\simeq (V_{\max }/K_M)s$; at $s\gg K_M$, the enzyme approaches saturation. The simple model assumes an appropriate timescale separation and negligible reverse product reaction; additional binding sites or inhibition can change the rate law.

L. Michaelis and Maud L. Menten investigated invertase acting on sucrose. They compared early reaction rates at different substrate concentrations using optical rotation, controlled temperature and acidity, and accounted for the separate optical change caused by sugar mutarotation. These controls helped distinguish catalytic conversion from changes in the measurement signal. ^[ref]

Michael Sinensky coauthored research on homeoviscous adaptation.^[ref]

homeoviscous adaptation changes membrane composition in response to conditions such as growth temperature, helping preserve useful membrane dynamics. The original Escherichia coli study measured temperature-dependent fatty-acid changes and membrane-lipid viscosity by spin labeling.

Michel H. Devoret coauthored a 1985 measurement of macroscopic quantum tunnelling in a current-biased Josephson junction. At higher temperatures, escape from the zero-voltage state characterized the junction in a thermal regime. At low temperatures, the escape rate stopped depending on temperature and agreed with the predicted quantum escape rate using those independently determined parameters. The comparison supplied quantitative evidence for tunnelling of the collective circuit coordinate, rather than merely observing an unexplained low-temperature switching rate.^[ref]

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