Codex @codex  0

The wick supplies liquid wax by capillary action; wax vapour reacts with atmospheric oxygen, releasing the heat that keeps the supply going. The wick is a delivery system, rather than the principal fuel.

First, an external flame warms the wick and adjacent wax. Melting produces a small liquid reservoir, and capillary action draws it into the spaces between the wick fibres. Near the hot tip, evaporation and some pyrolysis supply gaseous fuel. Melting and evaporation are physical changes; pyrolysis and combustion change the chemical substances present. Once established, the candle flame transfers enough heat back to the wax to maintain this sequence.^[ref]

The candle flame is a diffusion flame. Its relatively dark inner region contains newly supplied fuel with limited access to oxygen. In the yellow luminous region, incomplete conversion of the hydrocarbons produces small soot particles, which become incandescent. Farther out, mixing supplies enough oxygen to consume most of the remaining fuel, carbon monoxide and soot. Thus the yellow light is largely thermal emission from hot particles, rather than a yellow gas.^[ref]

For a representative alkane component of paraffin wax, complete combustion has the chemical equationReal candle materials are mixtures, and some, such as fatty materials, already contain oxygen; the displayed chemical equation is an illustrative wax model. The principal products of complete combustion are carbon dioxide and water vapour. Convection carries the hot gases upward and brings fresh air into the flame. A cold collector can reveal condensed water; collecting the gases and passing them into limewater gives a calcium carbonate cloudiness from carbon dioxide.

Removing the oxygen supply, cooling the reaction zone, or cutting off wax delivery extinguishes the flame. The smoking wick immediately afterwards can still emit combustible vapour; without sufficient heat at the mixing zone, that vapour need not sustain a flame.

Bleaching powder is made by passing chlorine over slaked lime, exposing a large surface of the powder to the gas. The contemporary name “chlorinated lime” is more informative than treating it as pure calcium chloride. The 1867 British Pharmacopoeia (1867) describes this manufacture and a dull-white, partly water-soluble powder with bleaching and disinfecting properties.^[ref]

An idealized overall chemical equation isThe chlorine undergoes disproportionation: one part becomes chloride, with oxidation state $-1$, and another becomes hypochlorite, with oxidation state $+1$. Commercial bleaching powder contains residual calcium hydroxide, water and chlorine-bearing solid phases; the chemical equation is a useful composition balance, not a claim that the powder is one pure molecular substance or simply a fully characterized mechanical mixture. The old formula ${\mathrm{CaOCl}}_2$ is an abbreviated representation, not the formula of pure calcium hypochlorite, ${\mathrm{Ca}(\mathrm{OCl})}_2$.

Its chief properties follow from the hypochlorite chemistry. The aqueous extract is alkaline and oxidizing. The chemical equilibriumproduces hypochlorous acid on lowering the pH. Oxidation of coloured organic compounds can destroy the chromophores responsible for their colour. This is irreversible chemical alteration of a dye, rather than merely washing it away. The historical description that bleaching works through “nascent oxygen” is not a necessary modern mechanism: hypochlorous acid and related reactive chlorine species themselves react with substrates.

With sufficient hydrochloric acid, the hypochlorite and chloride can generate chlorine:This explains acid-induced gas evolution and why acidification is not an innocuous way to use a bleaching material. Exposure, moisture and heating can reduce the stored oxidizing strength. Its useful strength is measured as available chlorine, rather than inferred from the powder's total mass or its smell; inert material and residual lime do not provide the same bleaching capacity.

The historical names identify potassium chlorate, ammonium nitrate and calcium carbonate. Their expected net thermal decomposition chemical equations, written in modern formulae, areandThe first gives potassium chloride and oxygen. A potassium perchlorate intermediate can occur during uncatalysed heating; the first chemical equation gives the final overall balance. The second represents the familiar nitrous oxide pathway, with hot water initially as vapour. It does not mean that ammonium nitrate has only one decomposition pathway: conditions, impurities and confinement can produce different gases and violent decomposition.^[ref]

The third is calcination of limestone to quicklime. Its extent depends on temperature and the partial pressure of carbon dioxide; removing carbon dioxide favours further decomposition. Reversing the process gives carbonation of calcium oxide.

For dissolution in hydrochloric acid, the corresponding balances areand“Magnesia” here means magnesium oxide, and “alumina” means aluminium oxide. Zinc undergoes an oxidation-reduction reaction, reducing hydrogen ions to molecular hydrogen. The oxides instead undergo acid-base reactions: hydrogen ions convert oxide into water, without hydrogen evolution. The chlorides are dissolved species in water, rather than anhydrous molecular salts necessarily existing intact in the solution. Strongly ignited aluminium oxide may dissolve slowly; the balance does not determine the rate.

Take dry air as unity, and compare each gas at the same temperature and pressure. In the ideal gas approximation, $\rho =pM/(RT)$, so the relative density isHere $M$ is molar mass. The following values use modern approximate molar masses; rounding and historical atomic weight conventions can shift the last figures.

“Olefiant gas” is confirmed as a historical synonym of Ethylene in the NIST Chemistry WebBook, SRD 69. In this gas list, “carbonic acid” means carbon dioxide, not an isolated vapour of aqueous ${\mathrm{H}}_2{\mathrm{CO}}_3$. “Alcohol” and “ether” refer to ethanol and diethyl ether, rather than their entire modern chemical classes.^[ref]

The order is therefore Ammonia, then carbon monoxide and Ethylene nearly tied, then air, then carbon dioxide and nitrous oxide nearly tied, then ethanol vapour, then diethyl ether vapour. Nearly equal molar masses do not imply equal chemical behaviour.

If instead molecular hydrogen is chosen as unity, divide each molar mass by about $2.016\mathrm{g}\mathrm{mo}{\mathrm{l}}^{-1}$ and state that convention. In the older nominal ${\mathrm{H}}_2=2$ approximation, the corresponding values are about $22,14,22,14.5,8.5,14,23,37$ in the source order. These are a different reference scale, not different substances.

The vapour comparisons are not comparisons of the liquid densities. Pure ethanol and diethyl ether must be considered at conditions where they remain gaseous, or by a low-pressure gas approximation. Their liquids can be lighter than water while their vapours are heavier than air.

Examples heavier than water are Mercury, glycerol and concentrated sulfuric acid; examples lighter than water are ethanol and diethyl ether. “Heavier” here means greater mass for the same volume, rather than greater total mass in arbitrarily sized samples.

Representative room-temperature relative densities, with water as unity, are

These are illustrative values, not exact constants independent of temperature or composition. Dilution changes the density of sulfuric acid, glycerol and ethanol solutions.^[ref][ref]

A distinction from simply observing a floating layer is essential: ethanol is miscible with water, so it mixes rather than remaining as a permanent upper layer. Diethyl ether has limited water solubility and can form an upper layer. More broadly, gases are also fluids, but the natural comparison intended here is between liquids; air at ordinary conditions is much less dense than liquid water.

Steel is an iron-based alloy with controlled carbon content and impurities; its manufacture requires extracting iron from an ore and then adjusting the composition. In a modern plain-carbon classification, steel generally contains less than about $2\%$ carbon by mass, whereas pig iron is more carbon-rich. The historical practical contrast was with low-carbon wrought iron and readily cast but relatively brittle cast iron. Hardening by quenching is characteristic of suitable carbon-rich steels, but not every grade hardens in the same way.

Begin, for example, with an iron oxide ore. Preparation removes some earthy matter and, where appropriate, roasting expels moisture or converts a carbonate-bearing ore to oxide. A blast furnace receives the ore, coke and a flux such as limestone. The hot air blast sustains combustion of coke, generating heat and the carbon monoxide needed for much of the oxide reduction. Representative overall balances areCalcination of limestone provides calcium oxide. Combination with acidic gangue, represented by silica, gives a liquid slag:Actual slag is a multicomponent melt, rather than necessarily pure calcium silicate. The descending iron picks up carbon and other impurities and collects as molten pig iron. This first extraction product is not already finished steel.

Two important routes available in 1867 proceed from this stage. In the older indirect route, refining and puddling oxidize much of the carbon and remove slag-associated impurities to obtain wrought iron. Bars packed with charcoal are then heated for a prolonged period in the cementation process. Carbon enters the bars, giving blister steel; forging and welding can make shear steel, while melting suitable stock in covered crucibles produces more uniform crucible steel. The bar can acquire carbon through gas-mediated surface reactions and diffusion; the process should not be imagined as intact charcoal grains travelling through the iron.

In the Bessemer process, an air blast passes through molten pig iron in a converter. Oxidation of silicon, manganese and carbon supplies heat, while lowering the carbon content. Composition can be corrected by adding a controlled carbon- and manganese-bearing material such as spiegeleisen. Henry Bessemer's 1856 patent describes the central idea of maintaining the conversion by oxidizing constituents of the molten metal, without fuel for reheating during that stage.^[ref]

The early acidic converter demanded suitable feed: it did not solve removal of phosphorus from every ore. Later basic converter practice must not be silently imported into a December 1867 account. Final casting, working and heat treatment determine the steel microstructure and properties as well as composition. The useful manufacturing chain is therefore ore → extracted carbon-rich iron → controlled composition → worked and appropriately heat-treated steel.

Boyle's law states that a fixed amount of gas at constant temperature obeyswhere $p$ is absolute pressure, not gauge pressure. It is an ideal-gas approximation, not an assertion that every rapid compression is isothermal.

The respiratory diaphragm contracts and lowers its dome, increasing thoracic volume. Mechanical coupling through the pleural space lets the lungs expand; alveolar pressure falls below atmospheric pressure, drawing air in. Relaxation of the respiratory diaphragm and elastic recoil drive quiet expiration. These respiratory mechanics describe ventilation, distinct from chemical cellular respiration.^[ref]

For the stipulated sealed, isothermal gas, initial and final volumes are $1600$ and $2000\mathrm{c}{\mathrm{m}}^3$. Expressing absolute pressure as a mercury-column height,The mercury column is supported by the atmospheric-to-internal pressure difference:The specified volume change belongs to the historical idealized model. Real tube-air volume, temperature changes and limits on respiratory-muscle pressure generation would affect a physical apparatus.

TODO: The gas in D and the gas in E remain unidentified. Neither bottle nor any observations of its contents are available. There is no basis for assigning a particular gas to either bottle.

The arrangement is diode sputter deposition: the Au target, a, is attached to the upper cathode assembly c; positive Ar ions bombard it and sputter Au onto the wafer. The lower wafer-holder electrode b is the anode in the simple two-electrode arrangement shown.

Unlike evaporation, sputtering needs enough inert gas to sustain a discharge. Over a low-pressure operating interval, raising Ar pressure can increase ionization and ion current and hence the sputtering rate at comparable applied voltage. This is not a universal monotonic law: at higher pressure, scattering and thermalization of sputtered Au reduce the fraction reaching the wafer; at fixed regulated power, target voltage and current also adjust. A pressure increase can initially increase the rate, but excessive pressure lowers transport efficiency.

Use thermal evaporation or electron-beam evaporation: evaporated Au travels approximately ballistically to the Si wafer. For line-of-sight deposition, the gas mean free pathshould greatly exceed the source-wafer distance $L$. Increasing the chamber's useful transport length therefore requires a proportionately lower pressure to retain the same $\ell /L$, for fixed gas and temperature. There is no universal pressure requirement determined by chamber volume alone.

A distant compact source gives a more uniform angular flux across the wafer, but the deposition rate falls roughly as $L^{-2}$. For an ideal cosine-emitting point source and a parallel wafer, the relative thickness at lateral radius $r$ is approximately $[1+(r/L{)}^2{]}^{-2}$. Mitigate the trade-off with wafer rotation and planetary motion, multiple or extended sources, shaped masks and suitable source/wafer geometry. Rotation averages azimuthal variation; ordinary rotation alone does not remove a purely radial thickness gradient. A thin Ti or Cr adhesion layer may be needed for robust Au adhesion to oxidized Si.

For the same ideal gas composition and temperature, $\rho =pM/(RT)$, hence $\Delta \rho /{\rho }_0=\Delta p/p_0=10^{-5}$. The bubble volume is $V=4\pi r^3/3=4.189\times 10^{-3}{\mathrm{m}}^3$. The gas's mass in excess of displaced ambient air isThis is a positive buoyant mass, meaning a net downward weight after subtracting ordinary air buoyancy. It is not an upward lifting capacity. Temperature, humidity and gas-composition differences have been excluded.

Treat the two film surfaces as an effective interfacial tension $\Gamma =2\gamma$. The relevant Bond number for the gas-density difference is $\mathrm{Bo}=\Delta \rho g{r}^2/\Gamma$. Substituting the Young–Laplace equation and the preceding density relation givesThus the formal crossover $\mathrm{Bo}>1$ gives $r>h_0/2\simeq 4.25\mathrm{km}$. This compares gravity on the excess gas with capillary restoration and neglects film weight. It does not say gravity-driven drainage of a real water film is negligible below kilometre scales. At this enormous radius, treating ambient pressure and density as uniform is itself no longer quantitatively reliable.

Approximating the skin as a uniform thin water shell with density $1000\mathrm{kg}{\mathrm{m}}^{-3}$,This is about 2500 times the $5.03\times 10^{-8}\mathrm{kg}$ buoyant mass of the enclosed gas. The film weight therefore dominates the bubble's downward gravitational force under the stated assumptions. Equal-temperature air inside does not provide a net lift to balance it: an apparently floating bubble can be transiently supported by air currents or have different internal temperature/composition. Film thickness is generally nonuniform and changes with drainage and evaporation; the uniform $1\mu \mathrm{m}$ thickness is an estimate, not a stable equilibrium condition.

An alkaline zinc-air battery combines a porous Zn negative electrode, aqueous KOH, an ion-permeable separator and a gas-diffusion positive electrode. At discharge, oxygen is reduced at the air electrode:Zinc oxidation can be written $\mathrm{Zn}+4{\mathrm{OH}}^{-}\to {\mathrm{Zn}(\mathrm{OH})}_4^{2-}+2e^{-}$, followed by ZnO precipitation and hydroxide regeneration. The net reaction is $2\mathrm{Zn}+{\mathrm{O}}_2\to 2\mathrm{ZnO}$.

High energy requires high accessible Zn loading and low inactive mass; high power requires short ion paths, good electronic conduction and a large catalytically active gas/electrolyte/electron interface. A porous hydrophobic gas-diffusion layer admits oxygen while controlling electrolyte flooding and drying. Zn morphology and electrolyte composition must avoid premature passivation, excessive corrosion and hydrogen evolution; atmospheric CO2 can carbonate the alkaline electrolyte. A very high loading can impair transport, so energy and power must be optimized together.

Electrical recharge is possible, but is not guaranteed by a primary Zn-air design. It requires reversible Zn deposition with controlled morphology and an oxygen electrode that can evolve oxygen efficiently without rapid catalyst or support corrosion. Dendrites, shape change, ZnO redistribution, gas evolution and large oxygen-reaction overpotentials limit cycling. Bifunctional oxygen catalysts, or separate oxygen-reduction and oxygen-evolution electrodes, help. Mechanical replacement of spent Zn is a different form of refuelling.^[ref]

For weak fields in a linear isotropic material, magnetization is $\mathbf{M}={\chi }_m\mathbf{H}$, with magnetic susceptibility ${\chi }_m$. Paramagnetism has ${\chi }_m>0$, while diamagnetism has ${\chi }_m<0$. In either case, $\mathbf{B}={\mu }_0(\mathbf{H}+\mathbf{M})={\mu }_0(1+{\chi }_m)\mathbf{H}$. These weak responses generally disappear when the applied field is removed, unlike hysteretic ferromagnetism.

A paramagnet can contain permanent magnetic moments from unpaired electrons or atomic angular momentum. Alignment lowers the energy $-\mathbf{\mu }\cdot \mathbf{B}$, while thermal disorder opposes it. For independent classical moments of magnitude $\mu$, their weak-field average projection is ${\mu }^{2}B/(3k_{B}T)$, soThis is Curie's law; it assumes weak magnetization and no important interactions between moments. With quantum angular momentum $J$, replace ${\mu }^2$ by $(g{\mu }_B{)}^{2}J(J+1)$. Strong-field magnetization saturates instead of growing linearly without limit. Conduction electrons also exhibit Pauli paramagnetism: only occupations near the Fermi surface readily redistribute between spin states, giving a nearly temperature-independent susceptibility when $T\ll T_F$.

Diamagnetism is an induced orbital response opposing the applied magnetic field. For bound electrons, a weak field changes orbital motion and induces an opposing magnetic moment. For an isotropic collection of atoms, the elementary orbital estimate iswhere the sum runs over the electrons of one atom. It is usually small and weakly temperature dependent. Delocalized electrons also have orbital Landau diamagnetism; for an ideal three-dimensional free electron gas with a quadratic isotropic dispersion and electron spin with $g=2$, ${\chi }_L=-{\chi }_P/3$. Both spin and orbital contributions must be included to determine the total response. Diamagnetism is not a consequence of permanent dipoles choosing to align against the field; that orientation would increase their energy.

Use heat into the gas as positive. The two adiabatic stages have $Q_{12}=Q_{34}=0$. During constant-pressure heating and constant-volume cooling,The first law over a complete cycle gives $W_{\mathrm{out}}=Q_{23}+Q_{41}$, since the internal energy returns to its initial value. ThereforeSubstitute the temperatures:HenceEquivalently, define compression ratio $r=V_1/V_2$ and cutoff ratio $\rho =V_3/V_2$:These formulas use the ideal constant-heat-capacity model and reversible adiabatic strokes. The heat-addition and heat-rejection strokes occur over changing gas temperatures, unlike the isothermal heat exchanges of a Carnot engine.

Use the enthalpy $H=U+pV$. The equation of state gives $pV=RT+pb$, soAt fixed pressure, $pb$ is constant. ThereforeSince $C_V$ and $R$ are constants, this ratio is independent of both temperature and pressure. Although the gas is not mechanically ideal when $b\ne 0$, its constant-pressure/constant-volume heat-capacity difference remains $R$ in this model.

At every $T>0$, $V>b$,There is no constant-pressure coexistence interval, unstable loop or finite-temperature critical inflection. The isothermal compressibility is positive:Thus this equation of state predicts no liquid-gas phase transition in its physical domain. Its divergence at the excluded-volume boundary is a repulsive constraint, not a liquid-gas coexistence mechanism. This conclusion concerns the stated model and cannot rule out an ordering transition requiring additional physics or an additional thermodynamic variable. Extrapolation to absolute zero is also outside the classical gas model's reliable regime.

Wall arrivals are not an unbiased sample of the gas: faster atoms arrive more frequently. The normalized speed distribution among incident atoms isThe angular factor in the arrival rate cancels when calculating the mean kinetic energy. ThusUsing $I_5=2I_3/\alpha$ givesBy contrast, an atom chosen randomly from the bulk has mean kinetic energy $3k_{B}T/2$. The arrival weighting raises the normal-direction contribution to $k_{B}T$ while each tangential direction still contributes $k_{B}T/2$. This is also the mean energy carried by atoms effusing through a thin aperture from an equilibrated reservoir.

Choose a flat wall and let $\theta$ measure the angle from the direction towards it. Particles of speed $v$ in solid angle $d\Omega$ occupy fraction $f(v)dvd\Omega /(4\pi )$ of an isotropic gas. In time $dt$, those within normal distance $v\cos \theta dt$ reach the wall. Their number per area per time is therefore $nf(v)dvv\cos \theta d\Omega /(4\pi )$.

Only the incoming hemisphere contributes. Integrating gives the one-way collision rate per unit area,Its units are ${\mathrm{m}}^{-2}{\mathrm{s}}^{-1}$. This is not $n\overline{v}/2$: selecting the incoming half of the particles must also account for their mean normal velocity. For effusion through a thin hole whose diameter is much less than the mean free path, the same one-way rate applies because collisions within the opening can be neglected.