Learn All 59 finite-plan destinations are authored across thermal, entropy, optics, relativity, quantum and matter evidence, including two original composed synthesis investigations. Twenty investigation contracts,44 mixed tasks and a retained seven-version dossier support course-specific reasoning. Independent scientific and finite authored-scope review passed; authentic learner/practical evidence and institutional credit remain separate
This is the course outline. Open a unit to choose a lesson; every lesson opens on its own page. Explanations and experiments live inside those lesson pages.
Preparation: Calculus-based mechanics and electromagnetism; derivatives, definite integrals, vectors, differential equations and probability-density normalization. Prior AP or algebra-based physics supports preparation but does not confer completion credit for this distinct course.
Course outcome: Integrate velocity distributions into directional pressure, distinguish flux-selected observations, reconcile heat and work with temperature-dependent state energy, and test nonideal branch and calibration assumptions. Constrained entropy, finite-source work and thermal identifiability are also taught. Coherent fields, finite-aperture integrals, Jones and imaging matrices, sampled resolution and calibration evidence are authored. Event selection, worldline proper time and relativistic conservation/inference are authored. Quantum-state normalization, moments, phase, boundary and current evidence are authored. Atomic/solid-state, nuclear-decay and detector inference are authored. Composed optical/quantum/thermal and independently anchored frequency/event investigations connect all six categories through eight unfamiliar cumulative packets.
All lessons are directly accessible. Reused foundation explanations are identified where relevant; completing a different course does not award this course's evidence. The 59 registered lessons keep separate predictions, captures, practice responses and reflections.
Integrate velocity and speed distributions, distinguish flux-selected observations, reconcile heat/work with temperature-dependent state energy, and test nonideal and calibrated thermal models.
Retain two anisotropic recipes and the isotropic a=b=1 case. Derive the positive-half-space collision integral, compare mean velocity with mean square, and distinguish adding energy from redistributing it.
Derive the first two moments, retain cutoff and numerical-resolution roles separately, and explain why a normalized density need not be a validated physical model.
Normalize the speed-weighted density, compare first and second moments, and freeze a threshold-tail prediction before inspecting the curve. State which detector calibration would test a speed-independent-response premise.
Compare two temperatures at fixed activation scale and two scales at fixed temperature. Differentiate the proposed energy function and retain a regime where classical mode counting is an approximation.
Derive the correction, compare a split interval with the direct integral, and state why constant volume is necessary for the simple Q=delta U account in this packet.
Compute both path areas before revealing the ledger, close the two paths into a conceptual cycle and assign work/heat signs. Explain the reservoir and quasistatic assumptions rather than claiming a performed engine.
Compare states below, at and above the critical reduced temperature. Retain the excluded-volume domain, pressure sign and slope classification separately, and explain what additional evidence would be required for phase coexistence.
Bracket the root with the two starting temperatures, explain uniqueness from positive total capacity and compare a candidate midpoint residual with the solved residual. Change one initial temperature without changing the capacity law.
Fit the ideal model to one record, test it on the second, then fit the corrected model to both and freeze a third prediction. Retain the distinction between response-family validation and shared-gain identifiability.
Derive state-entropy and local generation integrals, enforce finite-reservoir constraints, distinguish heat input from net heat and test independently calibrated thermal hypotheses.
Retain two reference-path integrations and both heat/work accounts. Predict a compression and an expansion before checking; distinguish the gas state difference from total entropy generation.
Derive the unique energy root, integrate both capacity-over-temperature functions and retain their opposite signs. Reject a midpoint candidate using its energy residual; explain why arbitrary plotted candidates do not establish an entropy maximum.
Derive the model-consistency identity, retain ideal and nonideal endpoint predictions and explain why integrating equilibrium p dV along the displayed endpoint family would assign the wrong actual work.
Retain a four-row table of delta U, work and signed heat. Add gas entropy changes, then explain what external temperature-contact evidence would be required to calculate total generation.
Compare a rejected, exact-boundary and below-bound claim. Retain energy and entropy ledgers with explicit kelvin conversion; specify which unlisted input would change the model rather than rescue the original claim.
Derive the weighted geometric and arithmetic endpoints, compare their energy and entropy accounts and justify why irreversible common endpoints cannot deliver more work under the same boundary.
Derive the local expression, integrate it independently and reconcile both boundary fluxes. Change length while retaining boundary temperatures, and distinguish no storage from no production.
Fit useful and leak conductances with explicitly distinct records. Freeze both changed-temperature predictions, inspect the unused record, and propagate the direct prediction bound without double counting shared errors.
Integrate coherent fields and spectral envelopes, derive finite-aperture patterns and polarization projections, compose paraxial imaging matrices and separate resolution, calibration and unused evidence.
Reconstruct real and imaginary components before intensity. Compare a complete phase scan with a fixed reading, then change the beam ratio and derive visibility from the observed extrema.
Integrate the real and imaginary spectral terms independently, compare them with the analytic sinc, and distinguish intensity at a delay from a phase-scan visibility.
Track each interface coefficient and round-trip phase separately, then verify the full power sum and both zero-thickness and matched-index limits.
Integrate cosine across the aperture independently, verify the central limit and sign of successive amplitude lobes, then compare width changes without confusing normalized shape with power.
Hold separation fixed while changing width, then reverse the comparison. Retain both scales and enumerate exact missing orders before interpreting a fitted aperture geometry.
Sum real and imaginary components directly, compare with the geometric ratio away from its removable singularities and integrate a full q period to check the power scaling.
Carry real and imaginary components through each projection, compare both orders and explain why a changed relative phase alters the result despite unchanged component intensities.
Propagate all three rays explicitly through object-to-lens, lens deflection and lens-to-sensor stages. Compare with matrix multiplication and then solve B=0 without claiming diffraction-free real imaging.
Reconstruct the two shifted responses, integrate central and source-coordinate pixels independently and compare widths. Retain the one-dimensional averaging boundary and identify noise or unknown brightness as additional inference requirements.
Fit only the three assigned orders, derive the prediction weights and propagate bounds without assuming independent random errors. Freeze the unused prediction before comparing the fourth record and distinguish a failed model check from a unique diagnosis of its cause.
Construct event pairs and simultaneous slices, integrate proper time, derive velocity and signal transformations, close relativistic energy/momentum and test a boost using unused bounded evidence.
Transform all three supplied pairs, independently reconstruct the invariant and inverse transformation, and separate causal classification from an unsupported particle-velocity interpretation.
Construct both endpoint pairs, transform each explicitly and label which frame imposes simultaneity. Reject any purported length that uses different endpoint times in the measuring frame.
Reconstruct both positions and endpoint agreement, integrate each proper-time density independently and compare an average-velocity estimate with the actual integral.
Transform the explicit differential pair, calculate the ratio, reverse it and check the interval. Compare counter-moving and light cases before treating a sum as a massive-frame speed.
Reconstruct the invariant from two independently reported quantities, compare exact and approximate kinetic energies across speed and distinguish approximation error from input uncertainty.
Close total energy and momentum, independently reconstruct the composite velocity and mass, and partition the incoming kinetic energy before changing the target mass.
Derive the photon energy from the body invariant and independently close both total energy and signed momentum. Change fractional mass loss and compare the exact result with a no-recoil approximation.
Construct the two emission events and their different travel distances before taking a frequency ratio. Compare the fixed-clock and received-signal statements without assigning either to a cosmological model.
Derive both β derivatives, include the interior stationary point, freeze the training range and compare the unused coordinate intervals. Keep calibration changes, uncertainty revision and new-model proposals distinct from original validation.
Compare photon and matter-wave evidence, normalize position states and their moments, and solve introductory boundary, coherent-state and scattering problems with independent calibration and unused predictions.
Fit the two unknown-material records without using the generating work function or offset. Freeze the third prediction. Then add the independent reference material and recover the threshold. Change only the offset and identify which fitted quantities remain unchanged. Retain a gain-error alternative.
Derive the shift before checking three angles, including zero and 180 degrees. Reconstruct both recoil components and compare relativistic kinetic energy with the photon loss. State what independent target-state evidence is needed before applying the free-stationary-electron model.
Compare exact and nonrelativistic wavelengths at two energies. Hold energy fixed and change only aperture width until the first-zero existence condition changes. Retain the candidate sine even when the angle is withheld, then identify a separate energy or geometry calibration alternative.
Normalize the two pieces separately, verify continuity at the peak and compare two intervals that cross different branches. Move the peak without changing L and explain why N stays fixed while interval probabilities change. State which extra information would turn this into a stationary-state problem.
Derive normalization and both moments for two p values. Predict the direction of the mean-mode difference before revealing the graph. Compute one interval probability independently and explain what phase information remains absent.
Compare beta=0,+2,−2 at the same sigma. Retain the identical position curves, equal momentum spreads for opposite chirps and opposite covariance signs. Then halve sigma and predict the momentum change before revealing it. Explain why repeated sampling does not shrink the intrinsic state width.
Solve the two boundary equations before selecting n. Compare n=1,2,3 at fixed L and then change L at fixed n. Integrate one interval that does not end at a node, and distinguish normalization, stationary phase and energy measurement.
Predict local probability at phases 0,π/2,π before revealing it. Integrate the cross term over the entire well to verify zero and over a half-well to see why it survives. Compare a coherent preparation with an incoherent mixture that has the same energy populations.
Derive the matching equation from both continuity conditions. Retain the initial branch bracket and numerical residual for two depths, compare energy against the infinite-wall value and independently integrate the exponential tails. State what remains uncomputed about higher states.
Compare below, at and above threshold at the same width, then halve the width. Derive the threshold limit before checking it. Reconstruct a supplied unequal-lead current ratio and explain why the equal-lead shortcut cannot be exported to that problem.
Fit both hypotheses with exactly the same two records and freeze their third predictions. Propagate the original reading bounds with signed weights. Then design a separate left-quarter probability test and list one calibration or potential alternative that the available data still cannot exclude.
Use reduced-mass and radial-state reasoning, finite occupation sums, conditional material-response inference and nuclear population/energy ledgers; compare fresh evidence without overstating identification.
Derive the center/relative kinetic separation, calculate two finite-mass line positions and freeze the predicted difference. Add a common wavelength offset to both indications and compare the behavior of difference and ratio. Retain one unresolved multiplicative calibration alternative.
Normalize with the spherical volume measure and independently derive the cumulative law. Compare the two density modes with the mean, then change the scale at fixed physical radius and at fixed radius-to-scale ratio. Explain why these interventions differ.
Create a full label table for two shells and sum the magnetic labels rather than memorizing the total. Test an invalid l and identify which selected-state quantities must be withheld. Compare angular magnitude and projection without drawing a classical trajectory.
List all six configurations and normalize their weights for two temperature ratios. Reconstruct each level occupancy and total energy, then repeat with sixteen distinguishable configurations. Explain why a one-level occupancy greater than one would reject the spin-polarized fermion description.
Fit both two-parameter families with the same two records, keeping the mobility exponent independent. Freeze their third-temperature predictions and check positivity before logarithms. Change the assumed exponent and identify which inferred parameter shifts. Retain an independent-contact or temperature-calibration test.
Derive the analytic count integral and check it against numerical integration. Compare 160 and 320 panels for energy, labeling the difference honestly. Change mu and theta separately and distinguish a chemical-potential-controlled calculation from a fixed-particle-number problem.
Balance A and Z before computing Q. Compare positive and negative mass differences, identify the center-of-momentum threshold and withhold product partitions in forbidden cases. Then compute the separate binding ledger and explain why its reference state differs.
Derive the integrating-factor result and take the equal-rate limit before evaluating it. Verify inventory at initial time and two later times. Compare the daughter maximum condition in population and activity language, retaining explicit time units.
Invert total and background means independently and show the failed subtract-first calculation. Fit the first two corrected source means, freeze the third indicated response and compare it with the supplied fresh record. State why unknown efficiency, dead time or a changing background would weaken the inference.
Derive the energy and heat-capacity law from the geometric sum. Fit both amplitudes at the same temperature, retain two frozen predictions and propagate the direct calibration ratio. Then propose a temperature-dependent gain alternative and the independent measurement needed to test it.
Reconcile thermal, entropy, optical, relativistic, quantum and matter models across independent calibration stages; retain unfamiliar derivations, competing predictions, critique and revision without claiming real practical or learner certification.
Fit the two power standards, freeze the corrected pulse power and explicitly retain the independently supplied absorption premise. Derive the capacity integral, compare the constant-capacity alternative and calculate block entropy and absorbed mean photon count with units. Name the additional boundary information needed for total entropy production and a fresh capacity or gain observation that would challenge the chain.
Write the exact calibration and source records used by each fit. Freeze the independent-frequency and laboratory-duration predictions before viewing their checks. Propagate original-reading corners, identify shared-parameter correlations, and then complete a newly assigned six-category packet in the retained evidence workspace with prior exposure and assistance declared.
Keep predictions before comparison, complete raw records and units, explain competing models and test a changed case. Supplied and simulated data are labeled in each lesson. A saved notebook is not proof of experimental technique or correct reasoning.
Evidence to retain: Retain an anisotropic second-moment derivation, Gaussian normalization and independent cutoff/resolution checks, then derive a normalized flux-selected density and a changed threshold prediction. State what observation distinguishes bulk from detector-selected records.
Boundary: Original supplied distributions and virtual integrations. No gas handling or actual apparatus; distribution normalization does not verify equilibrium or detector response.
Evidence to retain: Differentiate the supplied activation energy, integrate a variable capacity over split intervals, compare two pressure paths between common endpoints and bracket a unique coupled-body equilibrium. Reconcile signs, units and each body energy separately.
Boundary: Positive supplied constitutive laws over finite temperature ranges, fixed-volume and quasistatic assumptions explicitly separated. No physical heating, cooling, vessel operation or measured practical evidence.
Evidence to retain: Retain pressure sign, excluded-volume domain, exact critical boundary and local derivative classification. Fit only assigned pressure records, freeze the unused prediction and propagate direct reading weights separately from shared-gain bounds.
Boundary: A homogeneous equation branch is not a full phase-coexistence construction. Unused generated records test internal model prediction, not independent apparatus performance or every shared bias.
Evidence to retain: Retain two reversible reference integrations with different heat/work, a nonlinear finite-body energy root and separate entropy changes, and an ideal/nonideal free-expansion comparison with a consistency identity. Freeze a changed endpoint and reject a false actual-work path.
Boundary: Supplied equilibrium constitutive laws and virtual endpoints only. No actual gas expansion, heating or practical observations. Unconstrained plotted candidates are not accessible isolated states.
Evidence to retain: Retain a four-leg signed heat/work table, separate positive input, test three two-reservoir claims and derive a finite-body reversible maximum from an entropy constraint. Compare direct-contact and work-extracting boundaries.
Boundary: Necessary thermodynamic conditions do not establish a working or safe device. No physical engine, pressure apparatus or performed instructional time is implied.
Evidence to retain: Derive local Fourier entropy production and integrate it into a boundary balance. Fit useful/leak pathways from genuinely separate records, freeze two changed-temperature predictions and retain direct correlated-error propagation plus a shared-gain limitation.
Boundary: Synthetic steady profiles and supplied power records, not measurements. Local equilibrium and response-family assumptions must remain visible; first-fit data are not fresh validation.
Evidence to retain: Retain complex field sums and visibility extrema; independently integrate the rectangular spectral phase; sum reflected beams and verify zero-thickness/matched-index limits and power closure.
Boundary: Original virtual lossless/coherent packets; no laser, intense-light source, alignment or practical apparatus operation.
Evidence to retain: Derive aperture integral/central limit, separate fringe/envelope scales, enumerate missing orders, verify finite-array period power and compare both orders of complex Jones projection.
Boundary: Scalar far-field and ideal monochromatic polarization assumptions; no copying of algebra-based course credit or actual experimental validation.
Evidence to retain: Compose matrices and propagate an actual ray family; integrate a supplied circular-response cut over pixel intervals; freeze a three-order fit and propagate exact linear-weight bounds before unused comparison.
Boundary: Paraxial ray model and one-dimensional sampled response are distinct approximations. Hard bounds are not confidence intervals, and unused synthetic data are not an independent physical measurement.
Evidence to retain: Transform three causal classes and invert the map; explicitly select simultaneous endpoint pairs in two frames; integrate two returning worldlines and verify equal endpoints but unequal proper times.
Boundary: Original flat-spacetime coordinates and idealized paths, not a real clock experiment or physical instantaneous reversal.
Evidence to retain: Derive velocity from transformed increments; close invariant mass, collision internal/bulk energy, photon recoil and arrival-time ledgers. Reconstruct a changed packet before public feedback.
Boundary: No actual particle source, radiation, accelerator, propulsion or laboratory procedure; c=1 numerical units retain distinct physical dimensions.
Evidence to retain: Freeze a boost interval inferred from a measured event-difference ratio, derive monotonic spatial and stationary time extrema, then compare independent unused coordinate intervals without refitting.
Boundary: Original hard-bound packet; marginal overlap is a necessary screen, not universal joint compatibility, probability or independent clock certification.
Evidence to retain: Fit a stopping line from two records, freeze a third and then use an independent reference material to separate offset and threshold. Derive Compton shift from vector momentum and relativistic energy. Compare exact/nonrelativistic electron wavelength and reject an unsupported aperture angle.
Boundary: Synthetic single-particle and instrument models; no ultraviolet, radiation, electron-beam or vacuum operation. Reference calibration and target-state assumptions are independent premises, not conclusions of a fit.
Evidence to retain: Normalize a piecewise amplitude with physical dx, integrate asymmetric moments, compare equal position densities with different phase chirps, derive well boundaries and integrate a coherent local probability. Contrast an incoherent mixture with the same energy populations.
Boundary: Original supplied quantum states and ideal Hamiltonians. Probability density, intrinsic spread, sampling error and individual trajectories remain distinct; no performed state preparation is claimed.
Evidence to retain: Bracket the lowest finite-well matching root and normalize both tails. Derive the barrier threshold limit and compare amplitude with current transmission. Fit two spectral alternatives with equal calibration budgets, freeze the third-level predictions and propagate the direct shared-record bounds.
Boundary: One-dimensional nonrelativistic matching models; no unique potential reconstruction, tunneling time or hardware evidence. Numerical brackets are floating-point diagnostics and bounded input errors are not statistical confidence.
Evidence to retain: Derive the reduced-mass shift for a changed mass pair, retain a common-offset alternative, integrate a changed radial sphere and enumerate a changed finite canonical state packet. Predict the difference between spatial mode, shell mode, mean and exclusion-limited occupancy before checking.
Boundary: Hypothetical Coulomb and finite-level states; no actual isotope identification, atomic imaging or spin preparation. State count is not occupancy.
Evidence to retain: Fit activation and contact families using the same two temperature records and independently fixed mobility exponent; freeze the third prediction. Integrate a bounded DOS with two quadrature resolutions, then calibrate classical and quantum heat-capacity amplitudes with one shared datum and compare unused temperatures with direct bounds.
Boundary: Conditional original response families, not measured band structure. A numerical resolution difference is not a certified quadrature error bound; fixed chemical potential is not fixed particle count.
Evidence to retain: Balance an abstract reaction ledger and reject a negative available-energy channel. Derive equal and unequal Bateman rates, check population versus activity at a peak, then correct synthetic steady-replica total/background means separately before fitting two ages and predicting a fresh third.
Boundary: Fictional mass and population records, virtual detector means only. No isotope activity/dose, reaction probability, real detector statistics or performed practical claim.
Evidence to retain: Fit independent optical standards,freeze pulse power and absorption premises,derive a finite-capacity temperature and entropy change,convert photon energy consistently,and compare a constant-capacity or gain alternative with a newly assigned packet.
Boundary: No physical source or material procedure. Block entropy change is not total entropy generation; exposed generated checks are not real measurements.
Evidence to retain: Fit only independent frequency anchors,freeze an unused calibration record,infer a Doppler parameter from a separate source and freeze an independent clock-duration test with original-reading corner bounds. Then complete a reviewer-frozen six-category assignment with retained first reasoning,actual criterion critique,revision and assistance/exposure declarations.
Boundary: Conditional affine response and flat-spacetime premises; deterministic corner bounds are not probabilities or a universal simultaneous-calibration certificate. Actual learner response and supervised practical gates remain separate.
Open the retained response and project workspaces. Practice, saved work and independently reviewed proficiency remain separate.
These 44 course-specific public tasks are practice, not a secure examination. Each retains up to three immutable written responses, known feedback exposure before each response, and human rubric critiques. Drafts remain editable. No text-length check or self-reported review certifies correctness, independence, laboratory skill or mastery.
Independent uniform velocity components have half-widths 300,200,100 m/s and mass density0.6 kg/m³. Derive all three normal pressures and translational energy density from integrals. If isolated relaxation at fixed density preserves only the total kinetic energy and becomes isotropic, find its scalar pressure. Explain why that number is not the original x-wall pressure.
Include calculations with units, source or dataset provenance, assumptions, competing explanations and limitations as relevant. The draft is saved but is not a locked response until submitted.
0/3 responses retained. No recorded feedback exposure for this task version. Earlier versions may already be familiar. Public inspectability still prevents certification of unfamiliarity.
At thermal scale s=300 m/s, compare bulk Maxwell mode,mean and RMS with the flux-selected mean and RMS. Derive the emitted tail above600 m/s and the ratio of emitted to bulk mean translational energy. Does that ratio prove the emitted sample came from a hotter reservoir? State why a finite Simpson normalization and a rigorous probability-tail bound address different errors.
Include calculations with units, source or dataset provenance, assumptions, competing explanations and limitations as relevant. The draft is saved but is not a locked response until submitted.
0/3 responses retained. No recorded feedback exposure for this task version. Earlier versions may already be familiar. Public inspectability still prevents certification of unfamiliarity.
For supplied Cv/R=1.5+T²/(T²+theta²), find Cv/R at T=400 K,theta=200 K and differentiate the taught energy primitive to check it. Separately two moles with Cv=20+0.01T J/(mol K) warm from300 to600 K at fixed volume. Find exact energy, the initial-capacity estimate, missed correction and the two contributions when split at400 K.
Include calculations with units, source or dataset provenance, assumptions, competing explanations and limitations as relevant. The draft is saved but is not a locked response until submitted.
0/3 responses retained. No recorded feedback exposure for this task version. Earlier versions may already be familiar. Public inspectability still prevents certification of unfamiliarity.
An ideal monatomic gas starts at1 litre,100 kPa and ends at2 litres,50 kPa. Find work and heat along an isotherm and along the straight pressure-volume line. Separately the reduced van der Waals model has t=.9,v=1: compute pressure,slope and formal compressibility, and decide what they establish. Compare with t=v=1.
Include calculations with units, source or dataset provenance, assumptions, competing explanations and limitations as relevant. The draft is saved but is not a locked response until submitted.
0/3 responses retained. No recorded feedback exposure for this task version. Earlier versions may already be familiar. Public inspectability still prevents certification of unfamiliarity.
Bodies with CA(T)=2+.01T J/K and CB=4 J/K start at400 and200 K under the taught isolated fixed-volume boundary. Derive the equilibrium equation and prove uniqueness between the initial temperatures. Compute the equilibrium and each body energy change. Would the result also establish the equilibration time or actual insulation?
Include calculations with units, source or dataset provenance, assumptions, competing explanations and limitations as relevant. The draft is saved but is not a locked response until submitted.
0/3 responses retained. No recorded feedback exposure for this task version. Earlier versions may already be familiar. Public inspectability still prevents certification of unfamiliarity.
Indicated pressures at1 and2 litres are16 and7 kPa. Fit Kfit/V+Afit/V² and freeze a3-litre prediction. Compare the ideal one-parameter fit using only the first record. Each calibration indication has independent deterministic error bounded.03 kPa; derive the direct third-prediction bound. If gain is independently bounded.98..1.02, find a gain-only interval for physical K and explain what that interval omits.
Include calculations with units, source or dataset provenance, assumptions, competing explanations and limitations as relevant. The draft is saved but is not a locked response until submitted.
0/3 responses retained. No recorded feedback exposure for this task version. Earlier versions may already be familiar. Public inspectability still prevents certification of unfamiliarity.
A gas has total Cv=15 J/K, nR=10 J/K. Endpoints are T1=300 K, V1=2 L and T2=600 K, V2=3 L. Compare fixed-volume heating then final isothermal expansion with initial isothermal expansion then heating: find delta S, delta U and both heats. Does either reference path prove the actual history was reversible?
Include calculations with units, source or dataset provenance, assumptions, competing explanations and limitations as relevant. The draft is saved but is not a locked response until submitted.
0/3 responses retained. No recorded feedback exposure for this task version. Earlier versions may already be familiar. Public inspectability still prevents certification of unfamiliarity.
Two constant-capacity bodies Ch=3 J/K, Cc=1 J/K start at 800 K and 200 K. Compare direct isolated contact with a reversible cyclic engine between them. Find both common temperatures, direct-contact entropy production and maximum extracted work. Explain why the lower endpoint does not violate energy conservation.
Include calculations with units, source or dataset provenance, assumptions, competing explanations and limitations as relevant. The draft is saved but is not a locked response until submitted.
0/3 responses retained. No recorded feedback exposure for this task version. Earlier versions may already be familiar. Public inspectability still prevents certification of unfamiliarity.
A supplied gas has U=20T−A/V joule and p=10T/V−A/V² kPa, V in litres, A=400 J L. It expands freely inside an insulated rigid enclosure from 400 K, 1 L to 4 L. Verify the consistency identity, find T2 and delta S, and compare the ideal A=0 prediction.
Include calculations with units, source or dataset provenance, assumptions, competing explanations and limitations as relevant. The draft is saved but is not a locked response until submitted.
0/3 responses retained. No recorded feedback exposure for this task version. Earlier versions may already be familiar. Public inspectability still prevents certification of unfamiliarity.
A monatomic ideal gas makes the clockwise rectangle p_low=80 kPa, p_high=240 kPa, V_low=1 L, V_high=3 L. Find each signed heat, net work and efficiency. Separately a cyclic device absorbs 900 J from 750 K and rejects to 300 K while claiming 600 J work. Test both laws for that separate device.
Include calculations with units, source or dataset provenance, assumptions, competing explanations and limitations as relevant. The draft is saved but is not a locked response until submitted.
0/3 responses retained. No recorded feedback exposure for this task version. Earlier versions may already be familiar. Public inspectability still prevents certification of unfamiliarity.
A steady slab has k=3 W/(m K), area 0.4 m², length 2 m and boundary temperatures 500/250 K. Derive the linear profile, heat rate, local entropy-production density and total generation. What changes when length doubles with the same boundaries?
Include calculations with units, source or dataset provenance, assumptions, competing explanations and limitations as relevant. The draft is saved but is not a locked response until submitted.
0/3 responses retained. No recorded feedback exposure for this task version. Earlier versions may already be familiar. Public inspectability still prevents certification of unfamiliarity.
With cold/ambient 300 K and hot 400 K, heater reads 360 W and independent cold calorimeter 240 W. Fit linear K, L. Freeze heater predictions at 550 K for a linear leak and for a quadratic leak L(deltaT)²/(100 K), both matching calibration. Each first reading has absolute error≤3 W; find K, L error bounds and the direct linear prediction bound. A fresh heater reading is 905±4 W: is it consistent with the linear prediction under these bounds?
Include calculations with units, source or dataset provenance, assumptions, competing explanations and limitations as relevant. The draft is saved but is not a locked response until submitted.
0/3 responses retained. No recorded feedback exposure for this task version. Earlier versions may already be familiar. Public inspectability still prevents certification of unfamiliarity.
First packet: coherent beam intensities 1 and 4, phase 180°. Derive intensity, extrema and visibility. Separate equal-beam flat-spectrum packet: carrier 10, full width 1, delay 0.5 in the stated units. Integrate normalized spectral phase and calculate the recorded intensity and visibility. Why can the two contrast mechanisms not be collapsed into one unexplained loss factor?
Include calculations with units, source or dataset provenance, assumptions, competing explanations and limitations as relevant. The draft is saved but is not a locked response until submitted.
0/3 responses retained. No recorded feedback exposure for this task version. Earlier versions may already be familiar. Public inspectability still prevents certification of unfamiliarity.
Film indices1/1.5/1 with vacuum wavelength600 nm and thickness200 nm: derive interface coefficients, round-trip phase and full R/T. Separately a normalized uniform slit has width3 and spatial frequency0.5. Derive field and intensity from the aperture integral. Do either local cancellation results prove that the source emits no power?
Include calculations with units, source or dataset provenance, assumptions, competing explanations and limitations as relevant. The draft is saved but is not a locked response until submitted.
0/3 responses retained. No recorded feedback exposure for this task version. Earlier versions may already be familiar. Public inspectability still prevents certification of unfamiliarity.
Original double slit w3,d4: find fringe spacing, first envelope zero and first missing order. Separate six-slit narrow array at q0.5: find sum and principal peak/nearest-zero spacing. For Jones input (1,−1)/sqrt2, compare45° then horizontal polarizers with the reverse order.
Include calculations with units, source or dataset provenance, assumptions, competing explanations and limitations as relevant. The draft is saved but is not a locked response until submitted.
0/3 responses retained. No recorded feedback exposure for this task version. Earlier versions may already be familiar. Public inspectability still prevents certification of unfamiliarity.
For f10 cm,a40 cm,b20 cm, multiply P(b)L P(a), compute determinant and the image-plane distance. For object height0.1 cm and angles−0.02,0,+0.02 rad, find sensor heights. Then explain why setting B=0 would not establish perfect resolution of two circular-aperture images. State the exact one-dimensional pixel operation and the additional evidence needed for a real two-source decision.
Include calculations with units, source or dataset provenance, assumptions, competing explanations and limitations as relevant. The draft is saved but is not a locked response until submitted.
0/3 responses retained. No recorded feedback exposure for this task version. Earlier versions may already be familiar. Public inspectability still prevents certification of unfamiliarity.
Fit only orders1/2/3 at6.4/12.4/18.4 mm. With gain anchor0.8±0.01 and each reading bound0.06 mm, derive slope/intercept, nominal wavelength and hard endpoints. Predict order4 before comparing24.6±0.06 mm. Does changing the gain anchor alter this held-out prediction in mm?
Include calculations with units, source or dataset provenance, assumptions, competing explanations and limitations as relevant. The draft is saved but is not a locked response until submitted.
0/3 responses retained. No recorded feedback exposure for this task version. Earlier versions may already be familiar. Public inspectability still prevents certification of unfamiliarity.
Before public feedback, choose a contrast, aperture or imaging claim and an alternative involving calibration, phase, source state or sampling. Define a virtual record that distinguishes them, an unused prediction, units and finite uncertainty. Derive at least one amplitude/integral/matrix relationship rather than importing a previous algebraic answer. No physical source or instrument procedure is requested.
Include calculations with units, source or dataset provenance, assumptions, competing explanations and limitations as relevant. The draft is saved but is not a locked response until submitted.
0/3 responses retained. No recorded feedback exposure for this task version. Earlier versions may already be familiar. Public inspectability still prevents certification of unfamiliarity.
Transform event difference (3,5) at β 0.8 in c=1 units; classify its interval and explain the reversed time order. Separately a rod has rest length 6 and laboratory speed 0.6. Construct lab-simultaneous and rest-simultaneous endpoint pairs and report which spatial difference measures laboratory length.
Include calculations with units, source or dataset provenance, assumptions, competing explanations and limitations as relevant. The draft is saved but is not a locked response until submitted.
0/3 responses retained. No recorded feedback exposure for this task version. Earlier versions may already be familiar. Public inspectability still prevents certification of unfamiliarity.
For T 10, a 0.6, derive proper times for the fixed-speed round trip and v(t)=a(1−2t/T). Then independently transform dt′ 1, dx′−0.5 from a frame moving +0.6. Compute dt, dx, u and check the interval. Why does neither zero net trip displacement nor a Galilean sum supply the required answer?
Include calculations with units, source or dataset provenance, assumptions, competing explanations and limitations as relevant. The draft is saved but is not a locked response until submitted.
0/3 responses retained. No recorded feedback exposure for this task version. Earlier versions may already be familiar. Public inspectability still prevents certification of unfamiliarity.
A mass 2 particle moves at 0.6: derive E, p, K and classical kinetic error. Separately a unit-mass projectile at 0.6 joins a stationary target of mass 2 with no escaping products. Find final total energy/momentum, composite mass/speed and internal versus bulk kinetic energy.
Include calculations with units, source or dataset provenance, assumptions, competing explanations and limitations as relevant. The draft is saved but is not a locked response until submitted.
0/3 responses retained. No recorded feedback exposure for this task version. Earlier versions may already be familiar. Public inspectability still prevents certification of unfamiliarity.
An initially stationary emitter M 3 loses rest-mass fraction 0.1 into one +x photon and one body. Derive photon energy, body rest/total energy, recoil momentum and kinetic energy. Separately a receding source β 0.8 emits with proper period 2. Find laboratory emission and arrival intervals and frequency ratio; distinguish its clock-rate ratio.
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Training event-difference ratio for a clock at rest in S is −0.6±0.02 in S′; absolute increments are not given. Infer boost bounds. For unused S pair (5,3), derive extrema of transformed coordinates over those bounds, then compare reported S′ pair (4,0.2) with coordinate hard errors ±0.05. Explain the role of an interior stationary point and why a central invariant discrepancy alone is not exact evidence of a violated invariant.
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Before public feedback, choose a clock, length or collision claim and a competing explanation involving event selection, frame sign, calibration or escaping energy. Specify a virtual unused record, derive its prediction, retain units and finite uncertainty, and plan actual critique/revision plus genuinely unfamiliar first reasoning. Do not propose physical source operation.
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Use a rounded stopping slope 0.4 V per frequency unit. Unknown-material indications at f8 and10 are1.3 and2.1 V; an independent reference with work function3 eV indicates1.2 V at f10. Fit the unknown line, freeze f12, and separate offset/work function. Separately a100 keV photon backscatters from a free stationary electron of rest energy511 keV; find outgoing photon energy and recoil kinetic energy. Why does an electron aperture use lambda=h/p rather than hc/K?
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A triangular amplitude has support length2 nm and peak fraction q=.25. Derive its normalization constant and probability left of x=1 nm. Separately the supplied beta-family density has p=3 on u0..1: derive mean,second moment,variance and mode. State why neither density alone specifies momentum statistics.
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For Gaussian sigmaX=.4 nm,beta=−1, find sigmaP/hbar in nm⁻¹, uncertainty product divided by hbar and covariance divided by hbar. Compare100 independent position preparations. Separately an electron well has L1.5 nm,n3 and energy coefficient.3760301626 eV nm²: find energy,interior nodes and left-third probability.
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For the equal n1/n2 coherent well state, derive probability in the left quarter for relative phase0 andpi. Compare an incoherent equal mixture and compute mean energy in units E1. Which observation distinguishes the phase-coherent state from that mixture?
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A finite symmetric well has an even matching solution z=pi/4,kappa a0=pi/4. Verify the match,find E/V0 and exterior probability from the taught normalization. Separately an equal-lead rectangular barrier at E=V0 has width parameter2; find T. For a different unequal-lead packet, transmitted amplitude squared .6 and right/left wave-number ratio.25 are supplied: find current transmission.
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Two spectral indications are y1=2,y2=5 eV at levels1,2. Fit quadratic-in-n and affine-in-n families and freeze their n3 predictions. Each input has independent hard bound±.02 eV. A fresh level reads10.02±.01 eV: compare each residual with its own combined bound. Separately compare uniform and ground-well density probabilities in the left quarter. Does a surviving model establish a unique potential?
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An ideal infinite-mass line wavelength is 600 nm. Nuclear/electron mass ratios are 1500 and3000; a common unknown additive wavelength indication offset is present. Find both physical wavelengths and heavy-minus-light difference; say what the offset cancels from and what a gain error would change. Separately a1s radial state has scale.08 nm: find mean radius, shell mode and probability inside.16 nm. Count spin-orbitals for principal shell n=3 and reject l=3 there.
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Two spin-polarized fermions occupy four nondegenerate states0, delta, 2delta, 3delta at q=exp(−delta/kBT)=1/2. Enumerate six pair weights, find the ground occupancy and total mean energy in units delta. Compare the ground occupancy for two distinguishable particles. Separately a constant DOS3 states/eV spans0 to 8 eV with mu=4 eV: find occupied count at any positive temperature and explain why f(mu)=1/2 is not itself that count.
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Log conductivity readings at 300 and600 K are−2 and ln(2)−1. Independently stipulated mobility exponent p=1. Fit A and Theta for L=A+p ln(T/300)−Theta/T, then freeze L at 900 K. What apparent Theta follows if p is incorrectly set to zero? Fit the same two records with resistance C+D/T and determine whether its900 K prediction is positive. Does either fit alone establish a unique band gap?
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Use the abstract (12, 6)+(4, 2) to(15, 7)+(1, 1) ledger. Rest-mass difference is−.004 u with 931.5 MeV/u and incoming center-of-momentum kinetic energy 5 MeV. Test feasibility and partition final energy with approximate mass ratio 15:1. Separately a chain has initial parent 800, daughter 0, lambda1=.1/min, lambda2=.2/min and time ln(2)/.1 min. Find parent, daughter, stable populations and both activities.
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For separately steady replicas, calibrated tau=.001 s. A background-only indication is 1000/51 per second. Total indications at nominal ages0 and2 s are 1000/11 and3000/53 per second. Correct all three means, fit the exponential source amplitude and rate, and freeze the total indicated rate at nominal age4 s. Explain why subtracting indications before inversion is wrong and why output count uncertainty is not automatically Poisson.
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An independently fixed oscillator Theta gives supplied factors Fcal=.8, Flow=.3, Fhigh=.95. The sole amplitude-calibration indication is 1.6±.02 response units. Freeze quantum and classical predictions at both fresh temperatures and their calibration-only hard bounds. Fresh low response is.61±.01. Assess each family under those bounds and name an unresolved gain alternative. Separately explain why a Fermi calculation at fixed mu need not preserve particle number.
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Independent uniform velocity components have zero means and half-widths100,200,300 m/s at mass density1.2 kg/m³. Derive all directional normal pressures and translational energy density from moments. If energy-preserving relaxation at fixed density becomes isotropic, find its pressure. Separately explain why effusive speed weighting cannot be interpreted as a hotter reservoir without correcting selection.
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Two isolated bodies each have constant total heat capacity2 J/K,initial temperatures600 and300 K. Compare direct thermal contact with ideal reversible work extraction ending at a common temperature. Derive final temperatures,total entropy change for direct contact and maximum extracted work. State which external energy/entropy boundary assumptions differ.
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For a uniform rectangular aperture,derive normalized far-field amplitude by integrating exp(iqx) over a symmetric width and show its first zero. Two equal apertures have center spacing three times their width: which noncentral interference order first coincides with an envelope zero? Separately a horizontally polarized input passes ideal45-degree then vertical polarizers; find transmitted fraction. Reverse the first element to vertical and explain the change.
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In c=1 units transform event difference(dt,dx)=(5,3) to a frame moving beta=.6. Classify the invariant and interpret the proper interval. Separately an emitter initially at rest with mass4 emits one +x photon and leaves a body of rest mass3. Find photon energy,recoil momentum,body total and kinetic energies; keep the two packets separate.
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A triangular amplitude on length L has peak fraction q=.75. Derive probability left of x=.5L and its normalization constant. Separately a normalized Gaussian has chirp beta=sqrt(3): find uncertainty product/hbar,covariance/hbar and covariance-corrected determinant/hbar². For an equal-lead barrier at exact threshold and width parameter3,find current transmission.
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A chain begins with1000 parents and no daughters. Parent rate is.4/min,daughter rate.2/min. At u=lambdaParent t=ln4,derive all populations and both activities; explain the daughter maximum. Separately a constant finite DOS4 states/eV spans0 to2 eV with mu1 eV. Find occupied number at any positive temperature and explain what would change in a fixed-number rather than fixed-mu calculation.
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Independent power standards10 and50 W indicate9 and33. A pulse indicates18.6 for10 s; independently justified absorption fraction.8. Use initial300 K and C(T)=2+.01T J/K. Fit power calibration,find incident/absorbed energy,final temperature and block entropy change. At supplied photon energy2.5 eV and conversion1.6e−19 J/eV,find absorbed mean photon count. Can the full entropy production be inferred?
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Frequency anchors2 and6 indicate2.7 and7.5. Before further data,freeze the indication expected at independent frequency4. A receding source with independently known rest frequency5 indicates3.3. Infer corrected source frequency,Doppler ratio,beta and laboratory duration for independently known proper duration6. Contrast the pulse arrival interval. State how original-reading bounds and a new six-category task should be retained before feedback.
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Reviewer identity and role are declarations, not authenticated credentials. Unsaved review fields below are lost on navigation. Review every criterion with an exact quotation, calculation or evidence citation and a next step.
Final synthesis proposal for the finite59-destination SC09 course. Coordinator retains all actual thermal,entropy,optical,relativistic,quantum and matter milestones and predecessor definitions; these concise domain milestones retain their actions while exact earlier definitions and learner histories remain archived; completion is never awarded automatically.
Retain the original distribution-to-pressure integral, Maxwell cutoff and resolution comparison, effusive selection normalization, variable-capacity state integral, two path-work accounts, nonideal branch decisions and independently calibrated pressure prediction. Reconstruct the new directional-moment exit packet before feedback.
Evidence to retain: Actual prior thermal derivations and records, preserved first reasoning, changed model checks and source/domain qualifications.
Retain reference-path entropy, finite-body constrained equilibrium, free-expansion model comparison, complete cycle heat/work ledger, reversible finite-source limit, local entropy-production versus boundary flux, and original-reading inference bounds. Defend the new direct-contact versus work-extraction packet.
Evidence to retain: Signed energy/entropy ledgers, absolute temperatures, reversibility and boundary premises, unused predictions and unresolved alternatives.
Retain coherent complex-field and finite-bandwidth evidence, film phase limits, aperture integral, double-slit envelope and finite-array distinctions, ordered Jones projections, imaging matrix, sampled resolution and calibration covariance. Derive the new missing-order and polarizer-order exit packet.
Evidence to retain: Original amplitude/integral/matrix work, independent versus shared calibration, source state, sampling limits and fresh optical predictions.
Retain selected event pairs, simultaneous endpoint constructions, worldline proper-time integrals, transformed differentials, invariant energy-momentum, collision/recoil budgets, arrival timing and unused boost bounds. Reconstruct the new timelike-pair and photon-recoil packet.
Evidence to retain: Actual event definitions and frame signs, invariant checks, internal versus bulk energy, original-reading uncertainty and unused records.
Retain reference-assisted stopping calibration, vector Compton conservation, matter-wave aperture existence, piecewise normalization and moments, chirped Fourier covariance, hard-wall and finite-well matching, coherent local probability, current transmission and equal-budget spectral tests. Solve the new asymmetric-state/chirp/threshold packet.
Evidence to retain: Original normalization and matching derivations, correct physical measures, phase and Hamiltonian limits, independent references and fresh comparisons.
Retain reduced-mass and radial-state derivations, angular label counts, canonical exclusion, activation/contact alternatives, bounded DOS integrals, nuclear mass/energy ledger, unequal/equal-rate chains, calibrated detector/background response and classical/quantum thermal comparison. Solve the new daughter-activity and finite-band packet.
Evidence to retain: Actual counts and measures, conditional transport interpretation, energy/population/rate closure, numerical diagnostics and withheld temperature or age predictions.
Use the new10/50 W standards and18.6 pulse indication packet,derive the finite-capacity and photon budgets,and retain missing entropy-boundary information plus one independently testable alternative. Separately use the new2.7/7.5 frequency anchors,freeze the independent frequency test,infer the source speed and derive event-duration versus arrival predictions. Propagate original-reading errors rather than independent fitted-parameter guesses.
Evidence to retain: Unchanged first responses,exact independent/fitted/fresh data roles,calibration fits,signed energy/entropy boundaries,corner or monotonic bounds,event definitions,limitations and frozen changed predictions.
An actual reviewer freezes an unfamiliar packet spanning thermal moments,entropy constraints,optical amplitude or matrix reasoning,relativistic events,quantum normalization/boundaries,and matter energy or population inference. Preserve first work,obtain criterion-linked critique,revise reasoning and then answer a different separately frozen transfer assignment. Declare prior exposure and assistance.
Evidence to retain: Actual first report,reviewer identity/role and evidence-linked critique,reasoned revision,exact new assignment and separate response. Test fixtures and public examples are never labeled real learner performance.
Retain raw-data identifiers, provenance, units, prior predictions, methods, calculations, competing explanations and safety boundaries. State explicitly when data are simulated, supplied or genuinely observed. This saved text cannot verify a real experiment; do not invent measurements or completed supervised work. Maximum 12,000 characters; retain larger evidence files separately and cite them.
A nonempty report is only a saved submission. First and revised reports remain separate and cannot be overwritten. A critique of the first report is required before retaining one revision.
Require a reviewer-frozen new packet with all six category claims,changed numerical and conceptual premises,at least one shared-calibration alternative and one unused prediction. Keep first reasoning before feedback;retain resources,assistance and prior exposure. Actual practical and institutional-credit gates remain external.
A human must supply the actual new task, evidence and conditions before the learner responds. The transfer-direction text is not itself an unseen assessment. Use the retained assignment form after the first project; exposed public task identifier: expanded-public:university-physics3.
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