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The chemical element with atomic number eighteen. Argon is a colourless noble gas. It can provide a protective atmosphere around hot, reactive materials, for example in welding, where excluding oxygen limits oxidation. Commercial production separates it by distillation of liquid air.^[ref]

Its discovery shows why a small disagreement can matter more than a reassuringly repeatable result. Two preparations can each give consistent measurements while producing different mixtures. The Rayleigh-Ramsay argon density experiment investigated just such a discrepancy. Gas density links the weighing to a mean molar mass; a separate separation process tests which component accounts for it.

Consider an original simplified model containing only nitrogen and argon, with argon mole fraction $x$. Let their molar masses be $M_N$ and $M_A$. Adding the component masses gives the mixture's mean molar massFor an ideal gas mixture at the same pressure and temperature as a pure-nitrogen reference, the gas density ratio isThe inversion requires known identities, the binary-mixture assumption and $M_A\ne M_N$. A density ratio cannot uniquely recover an arbitrary multicomponent mixture. Nor should $x$ be interpreted as the argon fraction of untreated air: the model sample has only the two specified components.

Choose round model values $M_N=28\mathrm{g}\mathrm{mo}{\mathrm{l}}^{-1}$ and $M_A=40\mathrm{g}\mathrm{mo}{\mathrm{l}}^{-1}$. For $x=0.010$, the calculated relative density excess isThus a one-percent mole fraction does not mean a one-percent gas density change. In a chosen $2.00\mathrm{L}$ globe at $100\mathrm{kPa}$ and $300\mathrm{K}$, the ideal gas law gives approximately $2.24508\mathrm{g}$ for pure nitrogen and $2.25471\mathrm{g}$ for this mixture: only $9.62\mathrm{mg}$ separates the weighings. These are model calculations with rounded molar masses, not historical measurements.

A direct control calculation explains why the filling conditions matter. At fixed pressure, pure nitrogen athas the same gas density as that mixture at $300\mathrm{K}$. A roughly $1.28\mathrm{K}$ mismatch can therefore imitate the entire stipulated composition signal. For small changes, the ideal gas law givesAn independently measured pressure and temperature, matched weighing procedure, and checks for residual vapour distinguish composition from these alternative causes. The model explains the need for controls; it does not supply the complete corrections for a real gas-weighing instrument.

Hot electrons can transfer energy to cosmic microwave background photons through Compton scattering. For a fixed electron fraction $x_e$ and electron temperature well above the radiation temperature, the optically thin gas cooling time scales approximately as $(1+z{)}^{-4}/x_e$. Its volume loss scales with electron density, not with $n_H^2$, because the radiation density is independent of local gas density. The process tends toward the radiation temperature; it heats rather than cools electrons colder than that radiation.

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.

Gas density is the mass density of a gas. For an ideal gas sample of amount of substance $n$, mean molar mass $\overline{M}$ and volume $V$, combine $m=n\overline{M}$ with $pV=nRT$ to obtainHere $R$ is the molar gas constant. For a homogeneous mixture of gases, $\overline{M}={\sum }_i{x}_i{M}_i$, where $x_i$ is the mole fraction of component $i$. Equal pressure and temperature make a gas density ratio equal to a mean-molar mass ratio within this model. Argon detection in a binary gas mixture gives a worked example and a temperature confounder.

A physicist whose research joined waves, optics, acoustics and precise measurement. He maintained a laboratory at Terling and served as Cavendish professor of experimental physics from 1879 to 1884. At Cambridge he developed laboratory courses; later he donated his Nobel award proceeds toward a Cavendish laboratory extension.^[ref]

The Rayleigh-Ramsay argon density experiment, pursued with William Ramsay, connects a small discrepancy in gas weighing to chemical separation. Its lesson is practical: agreement within one preparation method does not ensure that a second method produces the same chemical substance. The gas density model explains how composition and filling conditions both affect the readout.

A spherical bubble displaces liquid volume $4\pi a^3/3$. Neglect its own weight compared with the liquid buoyancy, as required by the stated gas/liquid approximation. Equating $4\pi a^3{\rho }_{l}g/3$ with the quadratic drag givesRetaining a nonnegligible gas density would add the factor $1-{\rho }_g/{\rho }_l$. Let $V_s=\sqrt{4ag/(3C_D)}>0$, so the upward slip is $u_1-u_2=V_s$.

With constant phase densities, adding the two volume balances gives ${\partial }_x[\alpha u_1+(1-\alpha )u_2]=0$. The closed lower end fixes the total volume flux to zero. Solving it together with the slip relation yieldsIndividual bubbles move upward for $0\le \alpha <1$, while small phase-fraction disturbances move at the characteristic speed $q^{\prime }(\alpha )=V_s(1-2\alpha )$. The latter is negative when $\alpha >1/2$: wave speed and bubble speed are different quantities.

A cleared region starts at the closed bottom, with ${\alpha }_L=0$ and ${\alpha }_R=3/4$. Its Rankine-Hugoniot condition speed is $[q]/[\alpha ]=V_s/4$. The intended clearing solution is thereforeIt is an entropy shock for the concave conservation law flux, since $q^{\prime }(0)=V_s>V_s/4>q^{\prime }(3/4)=-V_s/2$. Its speed also equals the bubble speed on its uncleared side, so it follows the last layer of bubbles. Under this continuation the last bubble reaches the outlet whenafter which $\alpha =0$ throughout the pipe.

There is a boundary qualification for this dense initial mixture. The characteristics in the uncleared state point into the pipe from the top. To continue the displayed solution all the way to the stated clearance time, its incoming top trace must remain $\alpha (1^{-},t)=3/4$ until clearing. Initial characteristics alone cover the shock only until $t=4/(3V_s)$, when its backward right-state characteristic first meets the top boundary. Atmospheric pressure by itself is not a boundary condition for this scalar phase-fraction equation. Thus the displayed formula and printed clearance time give the intended maintained-trace branch; a different top phase-fraction closure could change the later evolution. This is the incoming boundary condition in dense bubble clearing, and is separate from the local derivation of the conservation law.

In his 1895 lecture, Lord Rayleigh compared gas masses in a globe under matched pressure and temperature. Removing oxygen from air left gas about half a percent heavier than nitrogen prepared entirely from chemical sources. Several preparation routes reproduced the difference; hydrogen contamination was a concern. An eight-month storage test re-established the filling conditions: simply reweighing a sealed globe could not test a change in molar mass. William Ramsay concentrated the residual gas by circulating the mixture over hot magnesium, which consumed nitrogen. A spectral test checked remaining nitrogen. Agreement of spectra from this route and the alternative spark-and-alkali separation supported a common residual gas.^[ref]

The density difference alone identifies neither a unique chemical element nor its concentration. A heavier contaminant, a lighter reference contaminant, or unmatched filling conditions can all shift a weighing. A separation process and an optical spectrum provide additional observations. This combination makes the experiment powerful: the anomaly motivates another operation whose result can be checked independently.