A tiny change. A long energy journey.: sources & model

Look through a power plant, follow three separate water routes and trace energy across their walls. Balance the energy account, then investigate why a growing average can still hide empty trials.

What supports the explanation?

What this model assumes

1. Generic PWR topology and explanatory cutaway geometry, not a measured installation, complete piping diagram or operating simulator.
2. Water and energy markers are annotations with chosen presentation timing. No physical transit times, pressures, temperatures, flow rates or actual electrical power are computed.
3. The selected environmental cooling path is once-through. The contextual tower photograph depicts a different cooling arrangement and does not identify reactor type.
4. The MJ fractions are declared teaching choices. Rejection belongs to the whole conversion block; the zero-input fixture is not a shutdown transient.
5. The independent 0-or-2 branching model is mathematical. Its die probabilities, tokens and generations are not calibrated nuclear quantities or reactor operating controls.
6. The finite pseudorandom ensemble is illustrative. Theory and sample results remain separately labeled, and zeros remain in unconditional statistics.
7. Original NRC and USGS source images retain their distinct evidential scope and attribution. Their presence does not imply endorsement.
8. The paper activity has not been learner-trialed. It uses only paper, pencil and a die; it does not reproduce a physical nuclear process.
9. Which reactor architecture is modeled?: The scene is a generic PWR architecture with one representative primary loop, a secondary working-fluid circuit and a selected once-through cooling path. Real plants can have several primary loops and many support systems. A BWR instead produces turbine steam in the reactor vessel; do not transfer the separate-secondary explanation to it unchanged.
10. A model of connections, not a piping plan: The original 3D assembly expresses which components connect and which water systems remain separate in normal operation. Its shapes, sizes, rotations, marker speeds and path timing are authored for inspection. It calculates no pressure, temperature, flow rate, molecular transit time or real plant electrical power.
11. Energy amounts need a boundary: Let H be the supplied energy in MJ over an unspecified accounting interval. The chosen teaching fractions give gross electricity G=0.35H, electrical plant use U=0.03H, delivered electricity D=G−U and conversion-block rejection R=H−G. These fractions are not measured performance or a thermodynamic cycle calculation.
12. Three accounts, all closed: For H=100 MJ, G=35 MJ, U=3 MJ, D=32 MJ and R=65 MJ. The conversion block gives 100=35+65. Electrical delivery gives 35=32+3. If plant-use electricity eventually dissipates as heat, an enlarged boundary gives 100=32+(65+3). The 68 MJ total assumes no accumulating storage or other exports within that enlarged boundary.
13. Do not attach every rejected joule to one wall: The conversion block includes the secondary cycle, turbine and generator. R combines condenser rejection and other conversion losses. The plant animation identifies the condenser qualitatively; it does not label R as a measured condenser-only heat flow. Electrical-grid and auxiliary-supply wiring are not modeled.
14. MJ is not MW: MJ measures energy. MW measures energy per time: one MW is one MJ per second. The accounting exercise supplies no physical interval. A mathematical zero-input fixture therefore has zero outputs, but it is not a reactor shutdown model: stored thermal energy and continuing decay heat require additional states.
15. The counting-board rule: Each parent independently has two children with probability p, otherwise none. Cards use p=1/3, 1/2 or 2/3, represented by successful die faces 1–2, 1–3 or 1–4. Parents are replaced. Z₍g+1₎=2 Binomial(Zg,p). N is one or four independent starting families; g=0…8 is a generation count, not time.
16. Mean growth and extinction answer different questions: With m=2p, E[Zg]=N m^g. For one family let q₀=0 and q₍g+1₎=1−p+p qg²; then P(Zg=0)=qg^N. At p=1/2, N=1 and g=4, the mean is one but extinction probability is 0.7417297363. An average of one does not mean every trial has one token.
17. Why survivors look different: At those same parameters, the mean among surviving histories is E[Zg]/(1−P[Zg=0])≈3.871913. Removing empty rows changes the population being summarized. At p=2/3, even a growing mean permits immediate extinction with probability 1/3 for one ancestor; the eventual extinction probability is 1/2.
18. Replay is not resampling: The display records a seeded pseudorandom die outcome once for every parent and keeps every row. Pause, scrub and replay reveal the same history. A new trial changes the seed. Twenty separately seeded trials are a finite illustration; their sample averages need not closely match theory. An extinct row stays extinct.
19. Physical processes are not interchangeable: A prompt neutron is born near a fission event. A delayed neutron is born following decay in a particular fission-product chain. Moderation slows an existing neutron. Absorption without fission removes a neutron from the chain. Fuel-temperature feedback changes interaction probabilities. Decay heat is continuing energy release from radioactive products, separate from thermal energy already stored in material.
20. What the abstract multiplier does not establish: The mathematical m=2p is an expected count multiplier per generation in this invented process. It is not a reactor effective multiplication factor, neutron transport solution or power trajectory. Transport, external sources, precursors, physical timing, spatial/material dependence and thermal feedback are absent. Its controls never change the plant model.

What has been checked

Analytical reference cases, conservation or transition invariants, finite drawing commands, bounded setup parsing, discovery and route integrity are checked automatically. These checks do not establish anatomical fidelity, learner outcomes or browser/device compatibility. Independent subject review, learner trials, comprehensive accessibility review and browser video encoding checks remain pending.

Each source supports the associated claim. Sources do not certify this implementation or its visuals.

About the cover illustration

Original offline rendering of the lesson’s generic PWR geometry. Teaching colors distinguish separate water circuits; geometry and sizes are authored, not measured plant CAD. The cover omits transparent surfaces and labels. Original NRC and USGS source images are credited separately inside the educational evidence view.