= Piston-cylinder pressure apparatus
{title2=$p-p_{\rm ext}\simeq F/A$}
In a functional model, a driven <piston> reduces the chamber's <volume (thermodynamics)>. A surrounding cylinder carries the wall <stress>; a deformable packing or gasket closes a potential leak path around a moving or removable closure. A sample and a separate <pressure sensor> occupy the chamber. A transmitting <liquid> can load the sample on all sides; the sensor's signal passes to an external readout. This is a division of experimental functions, not a scale reconstruction of one historical machine.
For a slowly moving frictionless drive <piston> of effective <surface area> $A$, external <pressure> $p_{\rm ext}$ and inward applied <force> $F$, <Newton's second law> at mechanical balance gives
$$
F+p_{\rm ext}A-pA=0,\qquad p-p_{\rm ext}=F/A.
$$
Thus $20\,\mathrm{kN}$ on a stipulated $20\,\mathrm{mm^2}$ effective <surface area> corresponds ideally to $1\,\mathrm{GPa}$ of differential <pressure>. These are illustrative numbers, not apparatus specifications. The effective <surface area> is the one associated with the <pressure> difference, not necessarily an external ram's visible cross section. With resisting <friction> $F_f$ during inward motion, the balance becomes $p-p_{\rm ext}=(F-F_f)/A$. During outward motion the sign of the <friction> contribution reverses. An applied-load reading can therefore show <hysteresis> even when the chamber's actual <pressure> is well defined.
A <resistance pressure gauge> instead supplies an internal signal. In a generic electrical readout, measure an <electric potential difference> $V_e$ with a known <electric current> $I$ and use <Ohm's law> to infer <electrical resistance> $R=V_e/I$. This describes a possible readout principle; the lecture passage cited below identifies the sensor material and calibration landmarks without specifying this wiring.
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