= Adiabatic process
{wiki}
An <adiabatic process> has no <heat transfer> across the chosen boundary throughout the process: $\delta Q=0$, rather than merely zero net <heat> after incoming and outgoing transfers cancel. It is a condition on <energy> transfer, whereas an <isothermal process> holds <temperature> constant. A sealed cylinder can approach an <adiabatic process> through insulation or through motion short compared with the time needed for appreciable <heat transfer>. Its <temperature> can nevertheless change because <work> crosses the boundary.<Statistical Physics by David Tong/4 Classical Thermodynamics>[§§4.2–4.3: work, heat, and adiabatic legs of a cycle]{ref}
Take the trapped <gas> as a <closed system>, with fixed <amount of substance> and composition and no net change in bulk <kinetic energy> or <potential energy> between the endpoints. Define $Q_{\rm in}>0$ as <heat> entering and $W_{\rm out}>0$ as <work> delivered to the surroundings. The <first law of thermodynamics> gives
$$
\Delta U=Q_{\rm in}-W_{\rm out},\qquad
Q_{\rm in}=0\ \Longrightarrow\ \Delta U=-W_{\rm out}.
$$
Here $U$ is <internal energy>. An <adiabatic compression> normally supplies <work>, so $W_{\rm out}<0$; an <adiabatic expansion> against a resisting load delivers <work>, so $W_{\rm out}>0$. An <adiabatic process> need not preserve <internal energy> and need not make the <closed system> an <isolated system>. <Thermodynamics and Propulsion/2.5 Control volume form of the conservation laws>[MIT Unified Engineering, §2.5.2: heat inward and work outward in the first-law balance]{ref}
For a <reversible thermodynamic process>, $dS=\delta Q_{\rm rev}/T$ at positive absolute <temperature> $T$. A reversible <adiabatic process> therefore has $dS=0$: it is an <isentropic process>. Irreversible <adiabatic processes> can instead generate <entropy>; <free expansion> is the existing counterexample, with its calculation in <entropy change in free expansion>. Conversely, constant <entropy> alone does not certify an <adiabatic process> or reversibility: outward <heat> can export the <entropy> generated internally. For a <closed system> the macroscopic <entropy> balance is
$$
\Delta S=\int\frac{\delta Q_{\rm in}}{T_b}+S_{\rm gen},\qquad S_{\rm gen}\geq0,
$$
where $T_b$ is the absolute boundary <temperature> where each <heat> transfer occurs and $S_{\rm gen}$ is internal <entropy production>. With no <heat transfer>, this reduces to $\Delta S=S_{\rm gen}$; reversibility makes $S_{\rm gen}=0$. https://openstax.org/books/university-physics-volume-2/pages/4-6-entropy[Ling, Moebs and Sanny, University Physics Volume 2, §4.6: reversible heat and irreversible entropy increase]{ref}
A motivating experiment measures the <gas> <temperature> directly during compression and expansion, instead of inferring it from how warm a cylinder feels. PASCO's authored TD-8565 manual describes a sealed piston cylinder, a fine nickel-wire <thermometer>, an absolute <pressure> sensor and a position readout for <volume (thermodynamics)>. A computer records all three channels together. The wire's <electrical resistance> changes with <temperature>; its small size permits a rapid response. https://cdn.pasco.com/product_document/Adiabatic-Gas-Law-Apparatus-TD-8565-Manual.pdf[PASCO scientific, Adiabatic Gas Law Apparatus, guide 012-05110D, pp. 1–2: apparatus and readouts]{ref}
Use ordinary trapped air and the apparatus's designed travel stops; mount the base securely, close the valve during a stroke, and record the actual <volume (thermodynamics)> limits. John Hart's university demonstration uses a large transparent cylinder with a low-<heat capacity> <thermocouple>, a <pressure> sensor, a travel gauge and a safety stop. It explicitly keeps the release valve closed during the demonstration. The basic observable is a rise in <temperature> on compression and a fall on loaded expansion, alongside the corresponding <pressure> and <volume (thermodynamics)> changes. Hart discusses wall <thermal conduction>, sensor response and leakage as reasons real records differ from the reversible model. https://atoc.colorado.edu/TeachingandLearning/Demonstrations/AdiabaticExpansion/Adiabatic_expansion.htm[John Hart, University of Colorado (2000), Adiabatic Expansion and Gas Law Physics: sensor demonstration and limitations]{ref}
For a proposed rapid-versus-slow comparison, let the air and walls return to the same initial <thermal equilibrium> before each run, then compare the same starting and finishing <volume (thermodynamics)> values with different stroke durations. Read <temperature>, absolute <pressure> and position continuously, including the hold after motion stops. A rapid compression gives a temporary <temperature> rise; holding the smaller <volume (thermodynamics)> lets <heat> leave and the <temperature> approach the surroundings again. Slow compression in good thermal contact allows that <heat transfer> during the stroke and approaches an <isothermal compression>. Loaded expansion reverses the signs: the rapid stroke cools, while <heat> entering during slow motion reduces the cooling. PASCO explicitly supports rapid nearly <adiabatic processes> and slow <isothermal processes>; the matched-run controls here are a proposed extension, not a reported set of measurements. https://www.pasco.com/products/lab-apparatus/thermodynamics/gas-laws/td-8565[PASCO scientific, TD-8565 product documentation: simultaneous readouts and adiabatic/isothermal comparisons]{ref}
Insulation suppresses <thermal conduction>; it does not prove that <heat transfer> vanishes. As proposed controls, repeat the matched strokes with and without a removable insulating jacket, record room and wall <temperatures>, measure fixed-position drift, and check valve closure and seal leakage. Calibrate the <thermometer> and position readout independently, including any connected dead <volume (thermodynamics)>; account for the <heat capacity> of the probe rather than treating it as a passive observer. Hart explicitly identifies the small air sample relative to the probe and walls, sensor inertia and seal leakage as limitations. A fast display cannot eliminate those physical effects. https://atoc.colorado.edu/TeachingandLearning/Demonstrations/AdiabaticExpansion/Adiabatic_expansion.htm[John Hart, Adiabatic Expansion and Gas Law Physics: wall, probe and seal limitations]{ref}
There are two distinct timing requirements. Let $\tau_{\rm eq}$ describe internal equilibration, $\tau_{\rm probe}$ the <thermometer> response, $t_{\rm move}$ the stroke duration and $\tau_{\rm heat}$ the effective <heat transfer> <time constant>. A useful sufficient window for a resolved, nearly reversible <adiabatic process> is
$$
\tau_{\rm eq},\tau_{\rm probe}\ll t_{\rm move}\ll\tau_{\rm heat},
$$
with negligible <friction>. The left inequality permits a <quasistatic process> and a usable readout; the right limits <heat> leakage. A violent stroke may satisfy only the right inequality. PASCO reports a roughly $30$–$50\,\mathrm{ms}$ lag of its <temperature> channel behind the other channels, so apparent simultaneous samples require care. If no such window exists, analyze equilibrium endpoints with the <first law of thermodynamics>, and regard the path as approximate. https://cdn.pasco.com/product_document/Adiabatic-Gas-Law-Apparatus-TD-8565-Manual.pdf[PASCO scientific, guide 012-05110D, p. 4: temperature-sensor lag]{ref}
\Image[/adiabatic-processes-sensor-and-timescales.png]
{title=Direct <temperature> readout and a <heat transfer> <time constant> in an <adiabatic process> experiment}
{description=Original apparatus schematic and analytical fixed-<volume (thermodynamics)> relaxation model, not measured records. After a stroke and internal equilibration, the stipulated <Newton's law of cooling> model gives $[T(t)-T_b]/|T(0)-T_b|=\pm e^{-t/\tau_{\rm heat}}$. The positive and negative curves illustrate the holds after compression and loaded expansion. The drawing is a generic sensor arrangement, not a reproduction of a commercial device; it distinguishes the small probe from the walls and their possible <heat transfer>.}
The diagram's model is deliberately a hold after the stroke, when boundary <work> is zero. For constant whole-sample <heat capacity at constant volume> $C_V$ and effective thermal conductance $K>0$, it assumes
$$
C_V\frac{dT}{dt}=-K(T-T_b),\qquad
\tau_{\rm heat}=\frac{C_V}{K},\qquad
T(t)-T_b=[T(0)-T_b]e^{-t/\tau_{\rm heat}}.
$$
This is <Newton's law of cooling> with one uniform <gas> <temperature> and a fixed surrounding <temperature>; actual wall and probe dynamics can require more than one <time constant>. At $t/\tau_{\rm heat}=0.1$, the fraction of the initial <temperature> anomaly erased is $1-e^{-0.1}\simeq0.0952$; at one <time constant> it is about $0.6321$. These are analytical fractions, not experimental tolerances or evidence that the preceding stroke was reversible. Measuring the hold helps estimate <heat> leakage independently of the motion.
The usefulness of an <adiabatic process> is that it separates mechanical <work> from <heat transfer>. Its reversible limit connects <temperature> changes, mechanical stiffness and <entropy> in one model: <Rüchardt experiment> and <Clément-Desormes experiment> already use that connection to measure <heat capacity ratio>. The contrast with <free expansion> explains the deeper point: suppressing <heat> does not determine how much <work> is exchanged or how much <entropy> is produced.
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