= Gas-syringe dead-volume correction
{title2=$V=V_{\rm read}+V_d$}
In a <gas syringe>, the graduated barrel reading $V_{\rm read}$ can omit a fixed connecting or sensor <volume (thermodynamics)> $V_d$ occupied by the same sealed <gas>. For a common settled <temperature>, <Boyle's law> then requires
$$
p_1(V_{{\rm read},1}+V_d)=p_2(V_{{\rm read},2}+V_d),\qquad
\frac1p=\frac{V_{\rm read}}{C}+\frac{V_d}{C}.
$$
This second relation makes a graph of $1/p$ against $V_{\rm read}$ a straight line; its intercept divided by its <slope> estimates $V_d$ under these assumptions. Unequal <temperatures> between the barrel and the connecting space require a different correction, analogous to the <gas thermometer dead-space correction>.
For an original hypothetical example, let $V_d=1\,\mathrm{cm^3}$, $V_{{\rm read},1}=20\,\mathrm{cm^3}$, $p_1=100\,\mathrm{kPa}$, and $V_{{\rm read},2}=10\,\mathrm{cm^3}$. The total <volume (thermodynamics)> falls from $21$ to $11\,\mathrm{cm^3}$, so $p_2=100(21/11)\,\mathrm{kPa}\approx190.91\,\mathrm{kPa}$, rather than $200\,\mathrm{kPa}$. The omitted <volume (thermodynamics)> makes the total compression ratio smaller than the barrel-reading ratio. These stipulated values are independent of the manufacturer's apparatus correction and are not measurements.
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