Pirani Vacuum Gauge Heat Loss & Gas Calibration Formula

Venting a vacuum load-lock with Argon or Helium on an un-corrected N2-calibrated Pirani gauge blows viewport O-rings right off their clamps!

**Marcello Pirani’s (`1906`) Constant-Temperature Thermal-Conductivity Vacuum Gauge** holds a fine tungsten/platinum sensor wire at `T_w ~= 395` K inside a `T_0 ~= 295` K tube using an automatic Wheatstone feedback bridge! Across `10⁻³` to `10` mbar (`Knudsen molecular-to-transition regime`), gas molecules colliding with the hot wire carry away **Conductive Power `Q_{gas} = (P_{true} / C_f) * K_0 * (T_w - T_0)`** (`mW`, atop constant **Radiation + End-Support Loss `Q_{rad}`** mW), so the bridge reports **Nitrogen-Equivalent Indicated Pressure `P_{ind} = P_{true} / C_f`** (`mbar`)! Because heavy monatomic **Argon (`C_f ~= 1.62` in molecular flow; and even worse above `20` mbar viscous flow where Pirani output saturates flat!)** conducts `38%` *less* heat than Nitrogen (`C_f = 1.00`), an un-corrected Pirani gauge **under-reads true Argon pressure**—trick-locking PLC vent valves open until positive overpressure pops elastomer viewports!

Start on an `N_2`-Calibrated (`C_f = 1.00`) Pirani Gauge Tube—True_Chamber_Pressure `P_{true}` = 0.850 mbar (B2), Gas_Correction_Factor `C_f` = 1.00 (B3), Wire_Temp `T_w` = 395 K (B4), Tube_Wall_Temp `T_0` = 295 K (B5), Free-Molecular_Conductance `K_0` = 0.48 mW/(mbar·K) (B6), and Parasitic_Radiation/End_Loss `Q_{rad}` = 4.20 mW (B7). Ask the in-app assistant for a thermal-bridge energy-balance hint: Indicated Gauge Pressure equals `0.850` mbar (E2), Gas Heat Transfer equals `40.80` mW (E3), Total Filament Bridge Power equals `45.00` mW (E4), with `90.7%` active gas signal above the radiation zero-floor (E5)!

Pirani Wheatstone Filament Heat Balance & Gas Calibration Factor Formula

Validate `True_Pressure` in `[0.0005, 50]` mbar, `Gas_Correction C_f` in `[0.30, 3.00]`, `Wall_Temp T_0` in `[250, 350]` K, `Wire_Temp T_w >= T_0 + 30` K up to `550` K, `Sensitivity K_0 > 0.05` mW/(mbar·K), and `Radiation_Loss > 0.2` mW!

=LET(pt_m, B2, cf_g, B3, tw_k, B4, tz_k, B5, kz_s, B6, qr_m, B7, qg_m, (pt_m / cf_g) * kz_s * (tw_k - tz_k), IF(OR(pt_m < 0.0005, pt_m > 50, cf_g < 0.3, cf_g > 3, tz_k < 250, tz_k > 350, tw_k < tz_k + 30, tw_k > 550, kz_s <= 0.05, qr_m <= 0.2), "Invalid Pirani Input", ROUND((qg_m / (qg_m + qr_m)) * 100, 1)))

Argon Sputter-Gas Backfill (`P_true = 1.20` mbar, `C_f = 1.62`) Under-Reading Trap Check

Backfill with pure Argon to `B2 = 1.20` mbar (`C_f` B3 = 1.62) without switching the controller gas table: Indicated Display E2 reads only **`0.741` mbar** (`38%` too low!), proving why safety atmospheric vent interlocks ALWAYS pair a Pirani with a **gas-independent Capacitance Manometer / Piezo Diaphragm switch**!

=IF(ISTEXT(E5), E5, ROUND(B2 / B3, 3))

Further reading

• Arte Sheets Lesson — UHV Chamber Outgassing Load & Ultimate Base Pressure Formula
• Arte Sheets Lesson — Turbomolecular Pump Compression Ratio & H2 Back-Streaming