= Residual lung volume
{title2=RV}
\b[Residual lung volume], RV, is the gas remaining in the <lungs> after maximal expiration. It is smaller than the quiet end-expiratory <functional residual capacity> by the <expiratory reserve volume>:
$$
\mathrm{RV}=\mathrm{FRC}-\mathrm{ERV}=\mathrm{TLC}-\mathrm{VC}.
$$
Thus residual gas is not the <tidal volume> or a direct measurement of gas exchanged in one breath.<Standardisation of the measurement of lung volumes, 2023 update by Nirav R. Bhakta and others>[Definitions and subdivisions of lung volume; Figure 1]{ref}
For stipulated FRC 2.5 L and <expiratory reserve volume> 1.1 L, RV is 1.4 L. Since <spirometry> records changes rather than an absolute lung-gas baseline, exhaling into a spirometer cannot by itself identify the gas still inside.
The 1956 experiment by <Arthur B. DuBois> and colleagues made that hidden volume accessible through <body plethysmography>. Their apparatus combined an airtight chamber, a mouthpiece shutter, capacitance pressure transducers and an oscillograph. Respiratory efforts against the closed shutter related mouth-pressure changes to changes in chamber volume.<A rapid plethysmographic method for measuring thoracic gas volume by Arthur B. DuBois and others>[Pages 322–324, Method, Figure 1 and equations 1–7]{ref}
The physical idea follows <Boyle's law>. For a fixed gas amount at approximately fixed temperature, write
$$
PV=(P+\Delta P)(V+\Delta V).
$$
To first order in the small changes,
$$
V\simeq-\frac{P\,\Delta V}{\Delta P}.
$$
An original ideal calculation uses effective gas pressure 100 kPa, pressure increase 0.2 kPa and volume decrease 4 mL, giving $V\simeq2000$ mL. This estimates the gas volume at the instant of airway closure. If closure occurs at quiet end-expiration, the result corresponds to an FRC-level measurement; <expiratory reserve volume> must still be subtracted to obtain <residual lung volume>. Pressure equilibration, thermal assumptions and correct volume conventions are part of the physical measurement, not consequences of the algebra alone.
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