Balance volatile inventory without inventing an eruption threshold

1. Define the evidence and convention

Magma contains silicate melt, crystals and dissolved volatile species in proportions that can change during ascent. Pressure reduction can lower volatile solubility, allowing gas to form. Gas amount, expansion, escape, viscosity and conduit conditions interact; gas presence alone does not uniquely determine eruption style.

2. Connect mechanism and model

The invented closed inventory contains 100 kg dry silicate and a kg water. A stipulated capacity 0.5√P kg, with pressure P in MPa, limits dissolved water. Dissolved water is the smaller of total and capacity, and the remaining mass is exsolved. No water is created by decompression.

For a deliberately ideal volume comparison, exsolved water is treated as gas at 1200 K, molar mass 0.018 kg/mol and R=8.314 J/(mol K). Its volume is nRT divided by pressure in pascals. A dry-silicate reference volume 100/2500=0.04 m³ is added while dissolved partial volume is neglected. This is not a calibrated water-solubility or high-pressure real-fluid model.

Hotter, less polymerized melts generally flow more readily, while silica-rich, cooler or crystal-rich magma can have higher viscosity. Gas escape and fragmentation alter outcomes further. Lava, ash, pyroclastic density currents, gases and water-rich lahars have different transport and exposure pathways. No calculated gas fraction here defines a real eruption, blast or safe-distance threshold.

3. Reconstruct the worked packet

At water 4 kg and pressure 10 MPa, capacity is about 1.58114 kg, leaving 2.41886 kg gas. The ideal gas volume is about 0.13407 m³, much larger than its mass alone suggests; the dry-silicate reference remains 0.04 m³. These volumes are conditional approximations.

4. Predict and investigate

Predict first: Can gas volume increase during pressure reduction while total water mass stays constant?

Track dissolved plus gas mass across pressure settings, convert MPa to Pa and calculate the conditional gas fraction. Identify at least three omitted mechanisms that prevent this inventory from becoming an eruption predictor.

5. Test a changed case

Apply the evidence to a changed case

At total water 2 kg and pressure 100 MPa, what is the dissolved/gas partition?

Retain the evidence frame, calculations and assumptions before opening public feedback.

Compare a worked response

Capacity is 5 kg, so all 2 kg remain dissolved and gas is zero in this stipulated model. This does not prove that a real magma with other volatiles cannot erupt.

6. Retain a defensible evidence notebook

Preserve first predictions, map orientation, intermediate calculations, units, assumptions and alternatives. These maps, numerical packets and diagrams are original invented instructional cases, not surveyed sites or current hazard forecasts. Independent practical review and genuinely unfamiliar evidence remain separate learner gates.

Mechanism reference, checked 30 October 2026. Original prose, diagrams and numerical exercises. No physical loading, pressurization or field hazard exposure is requested.