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Identity and discipline: upload.wikimedia.org/wikipedia/commons/7/74/A_Third_Generation_Water_Bath_Based_Blackbody_Source_(IA_jresv100n5p591).pdf

A electrical engineer.^[ref]

An astronomer researching the cosmic microwave background.^[ref]

A physicist associated with the Lennard-Jones potential.

Homepage: www.npl.co.uk/our-people/jonathan-pearce

Josiah Willard Gibbs was a mathematical scientist whose work gave thermodynamics and statistical mechanics powerful geometric and analytical formulations. His studies of heterogeneous equilibrium connected the behavior of multiple phases and chemical components, while his later work developed a systematic account of statistical ensembles. He also helped establish the practical language of vector calculus.^[ref] His Gibbs free energy combines internal energy, pressure, volume, temperature and entropy as $G=U+pV-TS$. Under the appropriate fixed-temperature and fixed-pressure conditions, its minimization expresses equilibrium, turning a physical stability question into a variational problem.

A long wire with uniform current density $I/(\pi a^2)$ generates uniform heat per volume $H=I^2/({\pi }^2{a}^4\sigma )$. Radial steady conduction obeys $(r{T}_r{)}_r=-Hr/k$. Regularity at the centre removes a logarithmic solution, leaving the displayed parabolic temperature excess relative to the surface. Conductivity, electrical conductivity and current density are assumed constant.

Joule heating is the dissipative conversion of electrical work into internal energy in an electrical conductor. In a metal, the electric field supplies energy to charge carriers, which transfer it to the material. This makes an immersed resistor a useful calibrated heater and makes electrical resistance a source of losses in wiring. Wind-driven electric currents are a proposed source of heating of an inflated giant planet.

For a stationary, purely resistive Ohmic conductor, use the passive sign convention: $V$ is the terminal electric potential difference from the entry to the exit of positive electric current $I$. The absorbed electrical power and Ohm's law giveThe last two expressions assume $V=IR$ at the relevant material temperature. For constant electrical resistance and electric current over a duration $\Delta t$, the dissipated energy is $E_{\mathrm{diss}}=I^{2}R\Delta t$; otherwise use $E_{\mathrm{diss}}=\int V(t)I(t)dt$. In SI, $\mathrm{V}\mathrm{A}=\mathrm{W}=J/s$.^[ref]

Absorbed electrical power $VI$ is more general than Joule heating: a capacitor can store energy, a battery can change its chemical energy, and an electrical circuit can deliver mechanical work or emit light. Even a heated resistor need not show an indefinitely rising temperature: in a thermal steady state, its dissipated power leaves by heat transfer. With the heater inside a calorimeter boundary, electrical input crosses as work; the subsequent heat transfer to the room is a different term in the first law of thermodynamics.

In his paper published in 1845, Joule connected two copper receivers with stopcocks, filled one with compressed dry air, and evacuated the other with an air pump. He immersed the connected receivers in water in an insulated arrangement, stirred the water, and read a sensitive thermometer. He then opened the stopcocks, let the air redistribute, stirred again, and compared the water's temperature with its initial value. Alternating control trials accounted for effects such as stirring and evaporation. The observation was no detectable net cooling of the common bath, rather than a record of the gas temperature at every instant. ^{[ref] [ref]}

Joule also immersed the receivers and their connecting piece in separate water vessels. The source receiver cooled while the receiving side warmed, with nearly cancelling thermal effects. ^[ref]

This distinguishes local transient changes from the final observation for the combined apparatus. Insulating its outer boundary suppresses external heat exchange; it does not prevent heat exchange between the gas, the receivers and the water inside that boundary.

An idealized modern version can use two rigid chambers joined by a valve, with thermometers in the chambers and on the walls. Prepare one chamber with gas and the other evacuated, disconnect the pump, close the apparatus to matter exchange, and let the initial temperature settle. Record initial and final equilibrium pressure and temperature, along with the wall response. Repeated closed-valve runs can reveal drift and valve-actuation effects; independent heating calibrations can estimate the heat capacity of the participating apparatus. This is a proposed measurement protocol, not a claim of a particular measured result. Fast local readings can characterize the release, but they cannot replace the final equilibrium readings in the endpoint internal energy balance.

Joule's paper On the Mechanical Equivalent of Heat (1850) describes a copper vessel holding water and a brass paddle with stationary vanes. Descending lead weights drove its shaft through strings and pulleys; the vanes opposed simple co-rotation. A boxwood shaft segment reduced thermal conduction. He measured fall distances and initial/final temperatures, repeating twenty descents per run and disconnecting the drive for rewinding. Calibrated thermometers read the water and room.^[ref]

His matched resting trials retained the water amount, duration, surroundings and reading procedure, omitting paddle motion to estimate environmental heat exchange. A screen reduced thermal radiation from his body. His calculation included the vessel and paddle heat capacities, external pulley/string losses, descent kinetic energy and string elasticity; it acknowledged residual vibration and sound.^[ref]

The measured observable is a corrected temperature rise, interpreted through the participating heat capacity; it is not a direct view of molecular motion. The experiment tests whether measured mechanical input accounts quantitatively for thermal storage. Frictional warming by itself would establish neither the conversion factor nor the absence of heat exchange. A modern authored demonstration at UCSB instead measures crank turns and a cylinder's temperature with an electrical thermometer: the apparatus differs, but again both mechanical input and thermal response must be measured. ^[ref]

The Joule-Thomson coefficient is the local temperature response to changing pressure at fixed enthalpy and fixed amount and composition:It describes the equilibrium endpoints of a Joule-Thomson effect experiment meeting the steady-flow energy balance assumptions. With $\Delta p=p_2-p_1<0$, a sufficiently small drop gives $\Delta T\simeq {\mu }_{\mathrm{JT}}\Delta p$. Thus ${\mu }_{\mathrm{JT}}>0$ means cooling, ${\mu }_{\mathrm{JT}}<0$ warming, and ${\mu }_{\mathrm{JT}}=0$ no first-order change. At zero coefficient, a finite drop can still change temperature. For a chosen illustrative local value ${\mu }_{\mathrm{JT}}=0.20\mathrm{K}\mathrm{ba}{\mathrm{r}}^{-1}$ and $\Delta p=-0.50\mathrm{bar}$, the linear prediction is $\Delta T=-0.10\mathrm{K}$; these are stipulated numbers, not measured gas properties.

For a fixed-composition simple compressible system, the measurable form isHere $C_p$ is the whole sample's heat capacity at constant pressure and $\alpha$ its volumetric coefficient of thermal expansion; alternatively use molar volume and molar heat capacity consistently. An ideal gas has $\alpha =1/T$, so ${\mu }_{\mathrm{JT}}=0$. Its enthalpy depends only on temperature; positive heat capacity at constant pressure then makes any such finite throttle preserve temperature. A real gas can have either sign. For $C_p>0$, compare $T\alpha$ with one: the thermal expansion response decides the sign, not insulation alone.^[ref]

A short derivation uses $dH=TdS+Vdp$ and the Maxwell relation $(\partial S/\partial p{)}_T=-(\partial V/\partial T{)}_p$:Setting $dH=0$ gives the coefficient. These are equilibrium state function identities, not a claim of a reversible thermodynamic process inside the throttle. For a finite drop, solve the endpoint enthalpy equality or integratealong the constant-enthalpy equilibrium curve. The coefficient can change sign during that integration, as the Van der Waals throttling model illustrates.

The Joule-Thomson effect is the temperature response of a fluid flowing from higher to lower pressure through a valve or a plug of porous medium, when the throttle is insulated and the other steady-flow energy balance assumptions hold. Its equilibrium endpoints have equal specific enthalpy. The Joule-Thomson coefficient determines whether a small drop cools or warms; cooling is not universal.

A useful contrast is between three insulated expansions. In free expansion of a gas-only closed system into a vacuum, no external work occurs and $U_2=U_1$; an ideal gas returns to its initial equilibrium temperature. In a throttle, continuous flow carries pressure work across the boundary and preserves specific enthalpy under the stated assumptions; an ideal gas again has no endpoint temperature change. In a reversible adiabatic expansion of a loaded closed system, the gas supplies work, loses internal energy and cools, even if it is an ideal gas. That process preserves entropy; throttling generally produces entropy. For a small constant-enthalpy step, $dH=TdS+Vdp=0$ gives $dS=-Vdp/T>0$ when $dp<0$ and $T,V>0$. This equilibrium comparison computes endpoint entropy differences without supplying a reversible path through the plug.

The effect is useful in refrigerators because an appropriately prepared real gas can cool while passing through a simple valve. The inlet must lie in a suitable positive-Joule-Thomson coefficient region. The Joule-Thomson inversion curve makes that requirement precise; a pressure drop by itself is not a guarantee of refrigeration.

The Joule-Thomson inversion curve is the set of equilibrium temperature–pressure states where the Joule-Thomson coefficient vanishes. For positive heat capacity at constant pressure, its condition is $T\alpha =1$, with $\alpha$ the coefficient of thermal expansion. The curve separates locally cooling and warming throttle regions. A finite isenthalpic process can cross it, so the inlet sign alone does not fix the total temperature change. An ideal gas has zero coefficient everywhere, rather than an isolated dividing curve.

A Joule-Thomson inversion temperature is a temperature at which the Joule-Thomson coefficient is zero at a specified pressure. There can be more than one such temperature at that pressure; distinguish the upper and lower branches from a maximum or a dilute-gas limiting value.

Julius von Mayer argued for a quantitative equivalence between mechanical work and heat. His 1842 paper connects compression of a gas with its heat capacity. In a modern ideal gas example, heating at constant pressure includes expansion work that is absent at constant volume. Because an ideal gas's internal energy depends only on temperature, its molar heat capacities satisfy $C_p-C_V=R$, where $R$ is the molar gas constant. The heat capacity difference thus supplies a route to comparing thermal and mechanical units of energy.^[ref]

Physician and natural philosopher who contributed to the conservation-of-energy programme in the 1840s, including an argument for the mechanical equivalent of heat.

A solid-state physicist who carried out physics research at IBM.^[ref]

On 10 July 1908, Heike Kamerlingh Onnes's Leiden laboratory circulated purified helium through liquid air and evaporatively cooled liquid-hydrogen precooling, a regenerative heat exchanger, and an expansion valve. Returning helium cooled incoming helium; liquid collected in a transparent vacuum vessel. Reflected light revealed its liquid meniscus, crossed by thermocouple wires. Subsequent mass density and spectroscopy checks tested contamination.^[ref]

A constant-volume helium gas thermometer below the valve supplied the temperature indication. An oxygen boiling reference check disagreed with its expected reading; the real gas correction to thermodynamic temperature remained provisional. A temperature plateau suggested immersion before the liquid meniscus was recognized.^[ref]

The measurement principles separate two questions. A visible liquid meniscus establishes an interface; a gas thermometer estimates temperature through an equation of state. A stationary temperature trace can also result from a steady state without phase coexistence, so it cannot replace the interface observation. Conversely, seeing a liquid does not calibrate a thermometer. Thermometer calibration, the gas thermometer dead-space correction, departures from the ideal gas law and incomplete thermal equilibrium all matter when assigning an absolute temperature. A check far from the intended measurement range tests the instrument but does not by itself bound every low-temperature error.

Kapitza resistance is the thermal boundary resistance encountered between a solid and helium in cryogenics. A cold helium heat bath can coexist with a warmer immersed component under continuous heating. The bath's temperature alone therefore does not establish the component's temperature. Kapitza thermal boundary experiment supplied an early direct demonstration of the obstacle at the solid–liquid boundary.

A microscopic route to interfacial heat transfer is transmission of phonons. Transmission depends on the two materials and their interface; scattering and the condition of the surface matter. ^[ref] The fourth-power thermal boundary model isolates one useful low-temperature limiting law without assigning an empirical coefficient to a particular sample.

Pyotr Leonidovich Kapitza's 1941 study suspended cleaned, annealed copper blocks in liquid helium. Sealed, gas-filled cavities held a heater and a bronze resistance thermometer. Electrical readout tracked the heating-induced temperature rise; the earlier readout method assumed a stable bath without a separate bath thermometer. A nearby unheated block warmed much less, localizing the drop near the heated surface. Gold plating and coatings tested surface effects; tight cavities prevented liquid ingress. These were solid-body readings, not probes resolving the microscopic interfacial layer. ^[ref]

The measurement logic suggests a modern control sequence: calibrate both temperature readouts, establish their zero-load difference, increase heater power, wait for a steady state, and repeat while monitoring the bath. Determine lead losses and the bulk temperature gradients before using $r_B=(T_s-T_l)/q$. These are proposed controls derived from the energy balance, rather than additional reported steps in the 1941 apparatus. A nearby unheated solid also has its own interface: its reading need not equal the liquid's local temperature exactly. The experiment supports a drop concentrated near the surface, while a microscopic thickness and a universal interfacial law require further evidence.