SCIENCE · INVESTIGATE AND EXPLAIN

Allocate energy to temperature change and phase fraction separately

Solve a piecewise fixed-pressure energy account rather than applying mcΔT through melting.

Learning outcome: For mass2 capture energies150,300,500 J. Identify stage, temperature and liquid fraction; repeat at mass1 and explain shifted thresholds.

Starting recap

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

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Try

For2 g, warming250→300 K requires200 J; another200 J completes melting. At total300 J, temperature300 K and liquid fraction.50.

Open the experiment

Predict

Must every positive heat input raise temperature while a pure substance melts at fixed pressure?

Your prediction and reason

Experiment

For mass2 capture energies150,300,500 J. Identify stage, temperature and liquid fraction; repeat at mass1 and explain shifted thresholds.

Allocate energy across warming and melting

Worked teaching model · synthetic values · Fictional solid starts250 K at fixed pressure; melting300 K, csolid2.0 J/(g K), latent fusion100 J/g, cliquid4.0 J/(g K). Loss-free quasistatic heating, no vaporization within the displayed final-temperature range. Coexistence has variable phase fraction at fixed300 K.

Energy supplied: 400 J Sample mass: 2 g

Reset keeps your prediction, captures and practice history.

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

energy supplied (J)	temperature (K)
0	250
25	256.25
50	262.5
75	268.75
100	275
125	281.25
150	287.5
175	293.75
200	300
225	300
250	300
275	300
300	300
325	300
350	300
375	300
400	300
425	303.125
450	306.25
475	309.375
500	312.5
525	315.625
550	318.75
575	321.875
600	325
625	328.125
650	331.25
675	334.375
700	337.5
725	340.625
750	343.75
775	346.875
800	350

Calculated evidence under the stated assumptions
Quantity	Value	Unit
Final temperature	300	K
Liquid mass fraction	1	fraction
Energy to reach melting	200	J
Energy to finish melting	400	J
Stage code	1	0 solid,1 coexistence,2 liquid

Coexisting solid and liquid exchange phase fraction at the fixed melting temperature.

The latent-energy interval does not raise temperature in this ideal fixed-pressure pure-substance model. Specific heat and latent heat have different units and roles. Cooling reverses the signed energy transfers; a mixture, changing pressure or supercooling could invalidate this simple path.

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

Coexisting solid and liquid exchange phase fraction at the fixed melting temperature.

Observation to attach to a capture

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

Understand

Separate sensible and latent energy

Within one phase, a constant-specific-heat model gives q=mcΔT. During ideal coexistence of a pure solid and liquid at fixed pressure, energy can instead change the phase fraction while temperature remains at the melting value. Applying the same mcΔT expression across that interval invents a temperature rise that the declared model does not predict.

Follow the supplied material

The fictional solid starts250 K, melts at300 K and has csolid=2.0 J/(g K). Warming each gram to melting therefore costs100 J. The latent fusion energy is another100 J/g, and the liquid specific heat is4.0 J/(g K). These are original stipulated values, not a named substance’s measured properties.

Work three energy ranges

For2 g, the first200 J warms the solid to300 K. Between200 and400 J, temperature stays300 K while liquid fraction grows from zero to one. At300 J total,100 J has entered the latent interval, giving fraction.50. At500 J, complete melting has used400 and the remaining100 J warms the liquid by100/(2×4)=12.5 K, reaching312.5 K.

Predict a mass change

For1 g, both warming and latent thresholds halve, but the melting temperature does not change in this ideal fixed-pressure model. The same total energy can therefore correspond to a different phase or temperature. A graph that rescales its axes should not be compared by screen slopes without reading the physical coordinates and units.

Transfer and boundary

A3 g sample receiving450 J has used300 J to warm and150 of the300 J fusion interval, so it is half liquid at300 K. Cooling reverses energy signs under the same equilibrium assumptions. Mixtures can melt across ranges, and changing pressure or nonequilibrium supercooling can alter the path. The model requests no heating and does not certify an actual material’s thermal limits or laboratory handling.

Sources and evidence boundary

Conceptual sources checked 30 October 2026: Phase changes, Heat capacity. 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

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

Which changing-pressure, mixture or nonequilibrium effects are absent from this ideal heating curve?

Your explanation and limitations

Continue

Completion requires a saved prediction, at least one capture and a reflection. Presence checks do not grade your reasoning.

Skipping retains experiments and awards no mastery.

Previous: Distinguish average bond energies from a reaction-specific enthalpy Next: Read a phase map as coexistence evidence rather than a heating trace

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