Measuring the Joule-Thomson effect with a porous plug (source code)

= Measuring the Joule-Thomson effect with a porous plug

The 2024 operating instructions for PHYWE's 04361-00 apparatus describe a frit between two gas chambers. A copper-coil <heat exchanger> first restores inlet <temperature> after cylinder-regulator cooling. An upstream manometer reads <gauge pressure>; the outlet stays at <atmospheric pressure>. Two NiCr-Ni <thermocouples> sit 2–5 mm from the frit. The digital meter's difference mode reports $0.01\,\mathrm K$ precision.<Joule-Thomson apparatus 04361-00, Operating instructions by PHYWE>[PHYWE, Joule-Thomson apparatus 04361-00, 2024 instructions, pp. 1–2, sections 2–4: heat exchanger, frit, manometer, probes and difference readout]{ref}

The manual specifies at most $1\,\mathrm{bar}$ <gauge pressure>, one hour of apparatus acclimatization, half an hour of meter warm-up, about 1.5 minutes of flow settling, then 10–15 seconds of averaging. It identifies a stagnant-gas zeroing error that shifts the fitted intercept and notes a maximum <nitrogen> signal of about $0.3\,\mathrm K$ in this setup.<Joule-Thomson apparatus 04361-00, Operating instructions by PHYWE>[PHYWE, 2024 instructions, p. 2, section 4, Hints concerning the experiment: pressure limit, equilibration, drift, averaging and zero compensation]{ref}

Define $x=p_1-p_2>0$ and $y=T_1-T_2$, so a small-drop fit is $y\simeq\mu_{\rm JT}x+c$. A constant sensor offset $c$ leaves the slope unchanged; pressure-dependent drift or <heat> leakage can alter it. The observable is the differential <temperature> slope across the plug, not cylinder-outlet cooling. Display precision alone does not establish accuracy or prove an <isenthalpic process>. This low-pressure, room-temperature apparatus does not map a complete <Joule-Thomson inversion curve>.