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In a functional model, a driven piston reduces the chamber's volume. 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 $p_{\mathrm{ext}}$ and inward applied force $F$, Newton's second law at mechanical balance givesThus $20\mathrm{kN}$ on a stipulated $20\mathrm{m}{\mathrm{m}}^2$ 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 $p-p_{\mathrm{ext}}=(F-F_f)/A$. 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.

A resistance pressure gauge is a pressure sensor whose electrical resistance is calibrated against pressure. Even a simple local response needs both pressure and temperature. For an original illustrative model definewhere $R_0$ is the reference electrical resistance at $p=0$, $T=T_0$, and zero history offset. The derivatives $\alpha$ and $\beta$ are local sensitivities with units $\mathrm{P}{\mathrm{a}}^{-1}$ and ${\mathrm{K}}^{-1}$, respectively; $h$ is a dimensionless history offset. Constant sensitivities are an approximation over a chosen range, not material constants valid at every pressure.

Choose synthetic coefficients $\alpha =0.020\mathrm{GP}{\mathrm{a}}^{-1}$ and $\beta =2.0\times 10^{-4}{\mathrm{K}}^{-1}$, with $T-T_0=10\mathrm{K}$ and $h=0$. A measured ratio $R/R_0=1.022$ then gives $p=(0.022-0.002)/0.020=1.00\mathrm{GPa}$. Ignoring the temperature change gives $1.10\mathrm{GPa}$, a $0.10\mathrm{GPa}$ error. This model is deliberately stipulated; these numbers are not measured manganin coefficients or Bridgman's data.

If two histories differ by $\Delta h=0.0004$, their outputs at the same pressure differ by $0.0004R_0$; interpreting both with a single history-free curve gives an apparent pressure separation $\Delta h/\alpha =0.020\mathrm{GPa}$. The half separation is $0.010\mathrm{GPa}$. Reversing the drive can additionally cause mechanical friction hysteresis, independently of this sensor model. Record both the electrical calibration history and the loading direction.

For independent small standard measurement uncertainties $u_y,u_T,u_h$ and exact stipulated $\alpha ,\beta$, first-order propagation givesFor $u_y=10^{-4}$, $u_T=0.5\mathrm{K}$, and $u_h=10^{-4}$, this is $u_p=0.00866\mathrm{GPa}$. Real calibration also includes coefficient measurement uncertainties, correlations, reference-point measurement uncertainty, and any unresolved nonhydrostatic loading. A sensor calibrates its local environment; it cannot by itself certify the absence of deviatoric stress throughout the sample.