SCIENCE · INVESTIGATE AND EXPLAIN

Distinguish cell charge capacity, loaded energy and internal conversion

An ampere-hour is a charge quantity, not an energy specification.

Learning outcome: Compare currents at the same elapsed time, close charge/capacity and all energy terms, and identify the exact capacity-exhaustion endpoint.

Starting recap

Refresh state-function boundaries, absolute temperature, dimensionless logarithms, written reaction/electron equivalents, conserved charge and formal orbital/identity bookkeeping.

All lessons are open directly. Your saved experiments remain when you leave and return.

Try

A1 A discharge for30 min passes1800 C. With emf1.50 V and internal resistance .20 ohm, external voltage1.30 V gives2340 J outside and360 J internally, totaling2700 J.

Open the experiment

Predict

Do equal ampere-hour capacities imply equal delivered energy for cells with different voltage histories?

Your prediction and reason

Experiment

Compare currents at the same elapsed time, close charge/capacity and all energy terms, and identify the exact capacity-exhaustion endpoint.

Close a finite virtual cell charge and loaded-energy account

Worked teaching model · synthetic values · Fictional constant-emf1.50 V cell with internal resistance .20 Ω and initial capacity1.00 Ah. Constant selected discharge current for up to30 min; allowed total charge≤capacity. Fixed emf/resistance are stipulated until depletion, not a real battery model, rating, heating or charging instruction.

Discharge current: 1 A Elapsed time: 30 min

Reset keeps your prediction, captures and practice history.

Remaining capacity versus elapsed minutes: solid

Axes rescale. A multiplicity distribution, inverse-temperature relation and charge-budget graph have different meanings. Read each axis and do not treat a computed curve as additional measured evidence.

All calculated plot coordinates

Remaining capacity versus elapsed minutes
elapsed minutes	remaining nominal capacity (Ah)
0	1
0.5	0.9916667
1	0.9833333
1.5	0.975
2	0.9666667
2.5	0.9583333
3	0.95
3.5	0.9416667
4	0.9333333
4.5	0.925
5	0.9166667
5.5	0.9083333
6	0.9
6.5	0.8916667
7	0.8833333
7.5	0.875
8	0.8666667
8.5	0.8583333
9	0.85
9.5	0.8416667
10	0.8333333
10.5	0.825
11	0.8166667
11.5	0.8083333
12	0.8
12.5	0.7916667
13	0.7833333
13.5	0.775
14	0.7666667
14.5	0.7583333
15	0.75
15.5	0.7416667
16	0.7333333
16.5	0.725
17	0.7166667
17.5	0.7083333
18	0.7
18.5	0.6916667
19	0.6833333
19.5	0.675
20	0.6666667
20.5	0.6583333
21	0.65
21.5	0.6416667
22	0.6333333
22.5	0.625
23	0.6166667
23.5	0.6083333
24	0.6
24.5	0.5916667
25	0.5833333
25.5	0.575
26	0.5666667
26.5	0.5583333
27	0.55
27.5	0.5416667
28	0.5333333
28.5	0.525
29	0.5166667
29.5	0.5083333
30	0.5

Calculated under the declared model
Quantity	Value	Unit
Charge delivered	1800	C
Remaining nominal capacity	0.5	Ah
Loaded terminal potential	1.3	V
Chemical ideal-emf energy decrease	2700	J
Energy delivered externally	2340	J
Internal resistive energy conversion	360	J
External plus internal energy	2700	J

The selected interval stays within the supplied finite charge capacity.

An ampere-hour is charge,3600 C, not energy. Under the supplied constant-emf model, source energy is emf times charge, while loaded electrical delivery is reduced by internal I²Rt. Real cells vary voltage, resistance, current efficiency and usable capacity with state and conditions. This virtual ledger does not specify a real battery rating or safe operation. Corrosion is also a redox process, but favorable potential alone does not determine its rate or passivation.

These calculated packets are not performed chemical measurements or separation procedures. Keep feasible inventories, activity conventions, fitting observations and independent checks distinct.

The selected interval stays within the supplied finite charge capacity.

Observation to attach to a capture

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

Understand

Start with a finite charge account

The fictional cell has nominal capacity1.00 Ah, equivalent to3600 C. At current I for t seconds, charge delivered is It and remaining nominal capacity is1−It/3600 Ah. The control grid does not exceed the supply; at2 A for30 min it reaches the exact endpoint.

This is a charge budget, not an assertion that every real cell sustains a fixed voltage to its last coulomb. Real usable capacity depends on current, temperature, history and chemistry. None of those are measured by this teaching packet.

Close source and load energy separately

The model stipulates emf1.50 V and internal resistance .20 ohm. Terminal potential is1.50−.20I. Ideal chemical energy decrease is emf times charge; delivered external energy is terminal potential times charge; the difference is I²Rt internal conversion.

At1 A for30 min, source energy is2700 J, external delivery2340 J and internal conversion360 J. Adding the latter two recovers the source amount. Treating all emf energy as external delivery would omit the internal boundary.

Corrosion also involves coupled oxidation and reduction, but favorable potential does not determine its rate, passivation or local transport. This model supplies no treatment or physical operation advice.

Transfer and check

At .50 A for20 min, Q600 C, terminal potential1.40 V, source energy900 J, external energy840 J and internal conversion60 J. Remaining capacity is5/6 Ah. Explain why a label of1 Ah alone would not have supplied any of those energy values.

Source and evidence boundary

Conceptual reference checked 30 October 2026: OpenStax Chemistry 2e. All prose, cases, graphs and questions are original. These supplied thermodynamic, electrical, nuclear or orbital models are not actual measurements, apparatus instructions, synthesis protocols or practical certification. Retain conventions, independent constraints, changed-case reasoning and limits. No heating, wiring, electrolysis, source handling or chemical manipulation is requested.

Apply

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

Why cannot the fixed-emf model certify the voltage curve, heat or usable capacity of a real battery?

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: Convert charge to a product only after electron and efficiency accounting Next: Separate nuclear bookkeeping, remaining parents and measured activity

Save a science backup or import one

Science work is stored locally in this browser, separately from mathematics and AI. It does not sync automatically. Use this science-only backup; this checkout's older all-subject export does not include science.

A legacy file is available only when the complete snapshot fits the 36 MB limit. For larger snapshots, prepare a complete file set below; never discard notebooks to make a smaller file.

Choose a science backup (maximum 36 MB)

Matching imported notebook drafts replace their current drafts. Omitted lessons and known first attempts remain. Export your current work first if you want to retain both drafts.

Complete file sets and course backups

A file set can hold more work than one science file. Keep its manifest and every part together. Each file is limited to 36 MB. This format needs this version of LearnAI or a compatible newer version; older versions can use only the legacy single-file backup above.

Export scope

The set includes every saved science course and global continuation at this moment. Later edits need a new export. A conflicting tab exports its own visible work, which may differ from saved work in another tab.

Choose the manifest and all parts together

0 file(s) selected. File order and filenames do not determine identity. Missing, changed or conflicting parts block the entire restore; no good part is applied by itself.

Science storage: loading. No account or remote computation is required.