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SCIENCE · INVESTIGATE AND EXPLAIN

Read a phase map as coexistence evidence rather than a heating trace

Keep pressure, temperature, coexistence and endpoint meanings separate.

Learning outcome: Compare350 K at pressures100 and300 kPa, then inspect the triple and critical coordinates. Trace a constant-pressure path below the triple point and describe which boundary it crosses.

Starting recap

Review signed energy transfers, dimensional consistency, reaction coefficients, state functions and phase/structural evidence boundaries.

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Try

The schematic triple point is300 K/100 kPa; the critical endpoint is500 K/800 kPa. A path below triple pressure has no stable liquid region in this map.

Open the experiment

Predict

Does crossing a liquid–gas coexistence line mean the material changed chemical identity?

Experiment

Compare350 K at pressures100 and300 kPa, then inspect the triple and critical coordinates. Trace a constant-pressure path below the triple point and describe which boundary it crosses.

Interpret a declared pressure-temperature phase map

Worked teaching model · synthetic values · Original schematic substance: triple(300 K,100 kPa), critical(500 K,800 kPa). Sublimation P=100 exp((T−300)/40) below triple; vaporization P=100 exp(ln8(T−300)/200) up to critical; fusion T=300+.020(P−100) above triple. Positive fusion slope. Not any real substance or a practical operating map.

Reset keeps your prediction, captures and practice history.

pressure (kPa)temperature (K)050010000

Axes rescale. On the phase map, short dashes show solid–gas coexistence, long dashes liquid–gas and the solid line solid–liquid; the dot is the selected state. In the Hess diagram, the dashed line is the independent direct packet. A heating plot follows supplied energy, not elapsed time.

Numerical diagram coordinates
temperature (K)pressure (kPa)
350300
solid–gas
temperature (K)pressure (kPa)
25028.65048
25532.46525
26036.78794
26541.6862
27047.23666
27553.52614
28060.65307
28568.72893
29077.88008
29588.24969
300100
liquid–gas
temperature (K)pressure (kPa)
300100
305105.3361
310110.9569
315116.8777
320123.1144
325129.684
330136.604
335143.8934
340151.5717
345159.6597
350168.1793
355177.1535
360186.6066
365196.5641
370207.053
375218.1015
380229.7397
385241.9988
390254.9121
395268.5145
400282.8427
405297.9355
410313.8336
415330.5801
420348.2202
425366.8016
430386.3745
435406.9919
440428.7094
445451.5858
450475.6828
455501.0658
460527.8032
465555.9673
470585.6343
475616.8843
480649.8019
485684.476
490721.0004
495759.4737
500800
solid–liquid
temperature (K)pressure (kPa)
300100
301150
302200
303250
304300
305350
306400
307450
308500
309550
310600
311650
312700
313750
314800
315850
316900
317950
3181000
Calculated evidence under the stated assumptions
QuantityValueUnit
Selected temperature350K
Selected pressure300kPa
Phase code21 solid,2 liquid,3 gas,4 single fluid,5 boundary,6 triple,7 critical
Triple temperature300K
Triple pressure100kPa
Critical temperature500K
Critical pressure800kPa

liquid

A line denotes coexistence under this schematic model, not a finite region of one phase. Below the triple pressure no stable liquid occurs in the represented path. Beyond the critical endpoint liquid and gas cease to be distinct phases. The positive fusion slope is not universal; water is a familiar counterexample. No actual operating range is implied.

Retain the system, phase and structural assumptions with every number. Supplied or calculated evidence is not actual calorimetry, chemical handling or X-ray operation.

liquid

A line denotes coexistence under this schematic model, not a finite region of one phase. Below the triple pressure no stable liquid occurs in the represented path. Beyond the critical endpoint liquid and gas cease to be distinct phases. The positive fusion slope is not universal; water is a familiar counterexample. No actual operating range is implied.

Captures preserve recipes and replay their calculated results. They are synthetic model evidence, not physical measurements.

Understand

Distinguish a map from a process trace

A pressure-temperature phase diagram summarizes equilibrium regions and coexistence boundaries. It is not temperature plotted against elapsed heating time or added energy. A process follows a path through the diagram only after pressure and temperature changes have been specified. Phase labels do not by themselves describe reaction rates or nucleation delays.

Use an explicitly fictional map

The supplied substance has a triple point at300 K and100 kPa, a critical endpoint at500 K and800 kPa and a positive-slope solid–liquid boundary. The curves are declared schematic functions, not fitted material data. Below the triple pressure, heating the stable solid can reach gas without an intervening stable liquid region; that phase change is sublimation rather than melting followed by boiling.

Read a boundary correctly

A liquid–gas boundary point permits coexistence of those phases, not an arbitrary finite region where every point must be a fixed50:50 mixture. The phase fractions depend on additional constraints such as total energy or volume. At the triple point three phases of the same component can coexist. Above both critical coordinates, liquid and gas are not distinct phases and the model labels a supercritical region.

Test a concrete path

At350 K the declared liquid–gas pressure is about168.18 kPa. A100 kPa point lies on the gas side; a300 kPa point lies in the liquid region, provided it is also beyond the melting boundary. Changing pressure at fixed temperature can therefore change the equilibrium phase without changing the chemical formula. The point exactly at the critical endpoint is labeled separately from a two-phase line.

Compare substances cautiously

The positive fusion slope is not universal: water provides a familiar negative-slope contrast near ordinary melting conditions. An original schematic must not be reused as a practical pressure/temperature operating chart. Retain the path, coordinate units, boundary crossing and omitted nonequilibrium effects. This activity calls for no sealed vessel, heating, cooling or real phase-transition experiment.

Sources and evidence boundary

Conceptual sources checked 30 October 2026: Phase diagrams. All prose, cases, code and diagrams are original. The supplied models are not measured structures, a performed laboratory investigation or certification of independent mastery. No chemical handling, heating, pressure vessel or cryogenic experiment is requested. Retain predictions, contrasting evidence and a changed-case explanation.

Apply

At a triple point in a one-component equilibrium phase map, which coexist?

Public practice checks a specific claim. It does not establish independent mastery.

Why can this original phase map not be used as an operating chart for a named substance?

Continue

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