Thermal radiation | PhysicsRank

You can feel warmth from a hot object without touching it. Radiation transfers energy across the gap, while the object also receives radiation from its surroundings. The cooling rate depends on that two-way exchange.

We will distinguish total power, net power and spectral peak, then connect the Stefan–Boltzmann and Wien laws through explicit assumptions about temperature, emissivity and geometry.

What you will learn to do

Explain radiative transfer through vacuum and exchange at equilibrium.
Distinguish blackbody, spectral and gray-body approximations.
Use actual emitting area and Kelvin temperature in total power.
Subtract surrounding radiation under a stated enclosure model.
Balance projected absorption against whole-surface emission.
Use wavelength-based Wien inference without confusing spectral representations.
Derive the small-excess-temperature radiation limit.

Useful before this chapterHeat balances, conduction and cooling →Exponential change, logarithms and controlled approximations →

Study with a tutor prompt

Copy this into your AI assistant, then describe where you got stuck. It asks the tutor to coach you one step at a time. Check its reasoning against the lesson.

Topic: Thermal radiation and the wavelength of a spectral peak
Learning goals:
- Explain radiative transfer through vacuum and exchange at equilibrium.
- Distinguish blackbody, spectral and gray-body approximations.
- Use actual emitting area and Kelvin temperature in total power.
- Subtract surrounding radiation under a stated enclosure model.
- Balance projected absorption against whole-surface emission.
- Use wavelength-based Wien inference without confusing spectral representations.
- Derive the small-excess-temperature radiation limit.

Start by checking the prerequisite idea I need most. Use a simple example, then change one condition to test my understanding.

Tutoring approach:
Act as a patient physics tutor. Ask what I understand and what I have tried, then wait for my reply. Teach one step at a time; do not give the final answer or a complete solution immediately. Start with a physical picture. Define unfamiliar symbols and operators, explain signs and units, and state the model's assumptions. Give progressively stronger hints only when I need them. Ask me to predict a change before calculating it. When I finish, help me check dimensions and a limiting case, then ask one related transfer question. If information is missing or ambiguous, ask rather than inventing it. Distinguish exact results from approximations and acknowledge uncertainty.

BEFORE YOU READ

Bring back one idea

Try a sentence or a sketch before opening the comparison. If this is new, use the explanation to get started.

Can an object emit radiation while having zero net radiative energy loss?

Compare your reasoning

Yes. At radiative equilibrium it absorbs as much power as it emits. Zero net exchange does not mean either process has stopped.

Revisit the explanation →

01 / Thermal radiation and the wavelength of a spectral peak

Thermal energy can cross a vacuum as electromagnetic radiation

A surface emits electromagnetic radiation associated with its temperature. Unlike conduction and convection, this transfer does not require a material medium between the emitting and receiving bodies. An object in a vacuum can therefore lose or gain thermal energy by radiation.

Emission and absorption happen at the same time. An object at the same temperature as its surroundings continues to emit, but in thermal equilibrium its absorbed power balances its emitted power. Zero net transfer does not mean zero microscopic exchange.

Radiation contains a range of wavelengths. At ordinary temperatures much of the thermal emission is infrared and invisible to human eyes. A surface’s visible colour alone therefore does not specify its absorption or emission across the thermal infrared range.

To calculate a thermal radiation balance, identify the surface temperature, emitting area, radiation arriving from the environment and the relevant material response. Geometry matters because an object can intercept a beam over a different area from the area over which it emits.

STOP & THINK

Two bodies separated by vacuum can exchange thermal energy by which mechanism?

Conduction through the empty space
Electromagnetic radiation
Bulk convection of the vacuum

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Study with a tutor prompt

Copy this into your AI assistant, then describe where you got stuck. It asks the tutor to coach you one step at a time. Check its reasoning against the lesson.

Topic: Thermal radiation and the wavelength of a spectral peak
Focus: Thermal energy can cross a vacuum as electromagnetic radiation
Learning goals:
- Explain radiative transfer through vacuum and exchange at equilibrium.
- Distinguish blackbody, spectral and gray-body approximations.
- Use actual emitting area and Kelvin temperature in total power.
- Subtract surrounding radiation under a stated enclosure model.
- Balance projected absorption against whole-surface emission.
- Use wavelength-based Wien inference without confusing spectral representations.
- Derive the small-excess-temperature radiation limit.
Equations in this section (LaTeX):
Build the physical reasoning before choosing an equation.

Start by checking the prerequisite idea I need most. Use a simple example, then change one condition to test my understanding.

Tutoring approach:
Act as a patient physics tutor. Ask what I understand and what I have tried, then wait for my reply. Teach one step at a time; do not give the final answer or a complete solution immediately. Start with a physical picture. Define unfamiliar symbols and operators, explain signs and units, and state the model's assumptions. Give progressively stronger hints only when I need them. Ask me to predict a change before calculating it. When I finish, help me check dimensions and a limiting case, then ask one related transfer question. If information is missing or ambiguous, ask rather than inventing it. Distinguish exact results from approximations and acknowledge uncertainty.

Back to chapter contents ↑

02 / Thermal radiation and the wavelength of a spectral peak

A blackbody is an absorption and emission model

An ideal blackbody absorbs all incident radiation at every wavelength and direction. In thermal equilibrium it also has the maximum thermal emission allowed for a surface at that temperature. It is a physical idealization, not simply the statement that an object looks black.

Emissivity compares a surface’s thermal emission with blackbody emission under specified conditions. A total hemispherical emissivity averages over wavelengths and outgoing directions; a spectral emissivity refers to a particular wavelength. Real emissivity can depend on wavelength, temperature and direction.

Kirchhoff’s law relates absorptivity and emissivity at the same wavelength and corresponding equilibrium conditions. A good absorber in one spectral region is also an effective emitter in that region. It does not justify equating a material’s sunlight absorptivity with its infrared emissivity when the spectra differ.

A gray-body approximation treats emissivity as sufficiently independent of wavelength over the relevant range. The simple net-exchange formulas used below adopt this approximation together with a large uniform surrounding enclosure. More complicated surfaces and view geometries require more detailed radiative exchange.

0\le\varepsilon\le1,\qquad P_{\mathrm{emit}}=\varepsilon\sigma AT^4

Here ε is the appropriate total emissivity for the stated surface model. T is absolute temperature and A is actual emitting surface area.

Study with a tutor prompt

Copy this into your AI assistant, then describe where you got stuck. It asks the tutor to coach you one step at a time. Check its reasoning against the lesson.

Topic: Thermal radiation and the wavelength of a spectral peak
Focus: A blackbody is an absorption and emission model
Learning goals:
- Explain radiative transfer through vacuum and exchange at equilibrium.
- Distinguish blackbody, spectral and gray-body approximations.
- Use actual emitting area and Kelvin temperature in total power.
- Subtract surrounding radiation under a stated enclosure model.
- Balance projected absorption against whole-surface emission.
- Use wavelength-based Wien inference without confusing spectral representations.
- Derive the small-excess-temperature radiation limit.
Equations in this section (LaTeX):
0\le\varepsilon\le1,\qquad P_{\mathrm{emit}}=\varepsilon\sigma AT^4
Meaning: Here ε is the appropriate total emissivity for the stated surface model. T is absolute temperature and A is actual emitting surface area.

Start by checking the prerequisite idea I need most. Use a simple example, then change one condition to test my understanding.

Back to chapter contents ↑

03 / Thermal radiation and the wavelength of a spectral peak

The Stefan–Boltzmann law describes power integrated over the spectrum

A blackbody surface emits power per area σT⁴, integrated over all wavelengths and outward directions. Multiplying by area and emissivity gives total emitted power in the simple surface model. The Stefan–Boltzmann constant is approximately 5.67 × 10⁻⁸ W/(m²·K⁴).

The fourth power makes absolute temperature essential. Doubling a Kelvin temperature multiplies emitted power by sixteen at fixed area and emissivity. Doubling a Celsius reading is not the same operation and cannot be used in that scaling.

Emitted power and net cooling power are different. The emitted term depends on the body’s own temperature; the net balance must subtract absorbed radiation and include any other transfer mechanisms. A body may emit strongly and still warm if it absorbs even more power.

The area is the sum of the surfaces that radiate under the model. A thin plate freely exposed on both faces has approximately twice its one-face area, apart from its edges. A sphere emits over 4πr², even when a distant parallel beam is intercepted over only πr².

WORKED EXAMPLE

Count both emitting faces of a plate

A thin plate has one-face area 0.020 m² and uniform temperature 400 K. Both faces have emissivity 0.50 and radiate freely; edge area is negligible. Use σ = 5.67 × 10⁻⁸ W/(m²·K⁴). Find total emitted power, without yet subtracting absorbed radiation.

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Study with a tutor prompt

Copy this into your AI assistant, then describe where you got stuck. It asks the tutor to coach you one step at a time. Check its reasoning against the lesson.

Topic: Thermal radiation and the wavelength of a spectral peak
Focus: The Stefan–Boltzmann law describes power integrated over the spectrum
Learning goals:
- Explain radiative transfer through vacuum and exchange at equilibrium.
- Distinguish blackbody, spectral and gray-body approximations.
- Use actual emitting area and Kelvin temperature in total power.
- Subtract surrounding radiation under a stated enclosure model.
- Balance projected absorption against whole-surface emission.
- Use wavelength-based Wien inference without confusing spectral representations.
- Derive the small-excess-temperature radiation limit.
Equations in this section (LaTeX):
Build the physical reasoning before choosing an equation.

Start by checking the prerequisite idea I need most. Use a simple example, then change one condition to test my understanding.

Back to chapter contents ↑

04 / Thermal radiation and the wavelength of a spectral peak

Subtract the surrounding radiation before predicting cooling

For a small gray body surrounded by a large black enclosure at uniform temperature T_a, with no intervening absorption and an effective view of the enclosure over its radiating surface, the absorbed power is εσAT_a⁴. Its net outward radiative power is εσA(T⁴ − T_a⁴).

The sign gives the thermal direction. If T > T_a, net radiation removes energy; if T < T_a, it adds energy. At equal temperatures the net term vanishes while emission and absorption individually remain nonzero.

For fixed surroundings, multiplying the body temperature does not generally multiply net power by the same fourth-power factor as emission. The ambient term stays fixed and must be subtracted in both states.

This expression should not be transferred automatically to two finite facing plates or an object seeing several different temperatures. View factors, multiple reflections and spectral differences can change the balance. State the enclosure and gray-surface assumptions when using the compact formula.

P_{\mathrm{net,out}}=\varepsilon\sigma A(T^4-T_a^4)

Small gray body in a large uniform black enclosure; no other transfer mechanism is included in this radiative term.

WORKED EXAMPLE

Compare net power while keeping the environment fixed

A gray body first has temperature 2T_a and then 4T_a, with the same area and emissivity inside a large black enclosure at T_a. Find the ratio of its new to old net outward radiative power.

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STOP & THINK

A body and a surrounding enclosure share the same temperature. Which statement describes radiative equilibrium?

Both emission and absorption cease
Emission and absorption continue at equal rates
The body absorbs but cannot emit

MEMBERSAnswer checking, feedback and the explanation are for members.Unlock →

Study with a tutor prompt

Copy this into your AI assistant, then describe where you got stuck. It asks the tutor to coach you one step at a time. Check its reasoning against the lesson.

Topic: Thermal radiation and the wavelength of a spectral peak
Focus: Subtract the surrounding radiation before predicting cooling
Learning goals:
- Explain radiative transfer through vacuum and exchange at equilibrium.
- Distinguish blackbody, spectral and gray-body approximations.
- Use actual emitting area and Kelvin temperature in total power.
- Subtract surrounding radiation under a stated enclosure model.
- Balance projected absorption against whole-surface emission.
- Use wavelength-based Wien inference without confusing spectral representations.
- Derive the small-excess-temperature radiation limit.
Equations in this section (LaTeX):
P_{\mathrm{net,out}}=\varepsilon\sigma A(T^4-T_a^4)
Meaning: Small gray body in a large uniform black enclosure; no other transfer mechanism is included in this radiative term.

Start by checking the prerequisite idea I need most. Use a simple example, then change one condition to test my understanding.

Back to chapter contents ↑

05 / Thermal radiation and the wavelength of a spectral peak

Match absorbed input to emission in a steady state

A steady temperature is found by balancing all input and output powers. For a uniformly warm sphere illuminated by a parallel beam of irradiance S, the intercepted power is Sπr² times the appropriate beam absorptivity α. Thermal emission occurs over the full area 4πr² with thermal emissivity ε.

If background radiation, conduction and convection are negligible, balance gives αSπr² = 4πr²εσT⁴. The radius cancels because both projected and emitting areas scale as r². This cancellation belongs to the uniform-temperature sphere model; it does not prove every point on a real illuminated sphere shares one temperature.

The ratio α/ε matters when the incoming spectrum differs from the thermal spectrum. A surface can absorb strongly in the incoming band but emit weakly in its own thermal band, giving a different temperature from a blackbody under the same illumination.

The geometry explains the factor four. It is not a universal radiation constant: a flat plate, a partially illuminated object or a body with large temperature differences needs a different area and balance model.

T=\left(\frac{\alpha S}{4\varepsilon\sigma}\right)^{1/4}

Uniform-temperature sphere, parallel incident beam, negligible background and other heat transfers. α refers to the incident spectrum and ε to the thermal emission spectrum.

WORKED EXAMPLE

Predict a temperature change without using an absolute irradiance

In the uniform-sphere model, the beam irradiance increases by a factor of sixteen while α and ε remain constant. What happens to the steady temperature?

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STOP & THINK

At fixed absorbed beam power and geometry, a body’s thermal emissivity decreases by a factor of sixteen. Under the same steady radiation-only model, what is the new-to-old Kelvin temperature ratio?

MEMBERSAnswer checking, feedback and the explanation are for members.Unlock →

Study with a tutor prompt

Copy this into your AI assistant, then describe where you got stuck. It asks the tutor to coach you one step at a time. Check its reasoning against the lesson.

Topic: Thermal radiation and the wavelength of a spectral peak
Focus: Match absorbed input to emission in a steady state
Learning goals:
- Explain radiative transfer through vacuum and exchange at equilibrium.
- Distinguish blackbody, spectral and gray-body approximations.
- Use actual emitting area and Kelvin temperature in total power.
- Subtract surrounding radiation under a stated enclosure model.
- Balance projected absorption against whole-surface emission.
- Use wavelength-based Wien inference without confusing spectral representations.
- Derive the small-excess-temperature radiation limit.
Equations in this section (LaTeX):
T=\left(\frac{\alpha S}{4\varepsilon\sigma}\right)^{1/4}
Meaning: Uniform-temperature sphere, parallel incident beam, negligible background and other heat transfers. α refers to the incident spectrum and ε to the thermal emission spectrum.

Start by checking the prerequisite idea I need most. Use a simple example, then change one condition to test my understanding.

Back to chapter contents ↑

06 / Thermal radiation and the wavelength of a spectral peak

A spectral peak is not the whole emitted power

A blackbody emits a continuous spectrum. The area under its spectral power-per-wavelength curve gives total power per surface area, while the wavelength of the curve’s maximum identifies where that particular spectral density peaks. Peak position and total area are different observables.

As temperature rises, the total blackbody power increases as T⁴ and the per-wavelength peak shifts toward shorter wavelengths. Wien’s displacement law expresses the second change: λ_max T = b, where b is approximately 2.90 × 10⁻³ m·K for this wavelength-based spectrum.

A body does not emit only at λ_max. A blackbody with a peak in the infrared still emits some visible radiation, and one with a visible-region peak emits a broad range of wavelengths. Apparent colour depends on the full spectrum and visual response, not just a single peak wavelength.

The peak depends on how the spectral density is represented. A spectrum plotted per unit frequency has a different maximum from a spectrum plotted per unit wavelength. In general, converting the wavelength peak through f = c/λ does not produce the frequency-density peak because the density transformation includes a Jacobian.

\lambda_{\max}T=b,\qquad b\approx2.90\times10^{-3}\ \mathrm{m\,K}

This is the peak of the blackbody spectral distribution per unit wavelength. A strongly wavelength-dependent emissivity can shift a real surface’s measured peak.

Study with a tutor prompt

Copy this into your AI assistant, then describe where you got stuck. It asks the tutor to coach you one step at a time. Check its reasoning against the lesson.

Topic: Thermal radiation and the wavelength of a spectral peak
Focus: A spectral peak is not the whole emitted power
Learning goals:
- Explain radiative transfer through vacuum and exchange at equilibrium.
- Distinguish blackbody, spectral and gray-body approximations.
- Use actual emitting area and Kelvin temperature in total power.
- Subtract surrounding radiation under a stated enclosure model.
- Balance projected absorption against whole-surface emission.
- Use wavelength-based Wien inference without confusing spectral representations.
- Derive the small-excess-temperature radiation limit.
Equations in this section (LaTeX):
\lambda_{\max}T=b,\qquad b\approx2.90\times10^{-3}\ \mathrm{m\,K}
Meaning: This is the peak of the blackbody spectral distribution per unit wavelength. A strongly wavelength-dependent emissivity can shift a real surface’s measured peak.

Start by checking the prerequisite idea I need most. Use a simple example, then change one condition to test my understanding.

Back to chapter contents ↑

07 / Thermal radiation and the wavelength of a spectral peak

Infer temperature only after identifying the spectrum and units

To infer a temperature from a wavelength peak, convert the wavelength to metres and apply T = b/λ_max. The inferred value assumes blackbody-like emission or an appropriate gray-body approximation over the relevant spectral range.

Comparing two blackbody peaks avoids the numerical constant: T₂/T₁ = λ_max,1/λ_max,2. If the peak wavelength halves, temperature doubles and total emitted power per area increases by sixteen. That combines Wien’s law with Stefan–Boltzmann, rather than treating them as competing formulas.

For equal total emitted power from blackbodies at different temperatures, the emitting areas must compensate for the fourth-power temperature dependence. A hotter smaller surface can emit the same total power as a cooler larger one, even though their spectra differ.

Before using a measured peak, check whether the detector reports power per wavelength, per frequency or some band-integrated response. Instrument sensitivity and absorption along the path can alter the measured curve. A peak in a detector’s raw counts need not be the source’s intrinsic spectral maximum.

WORKED EXAMPLE

Connect a wavelength peak to temperature and power scaling

A blackbody’s spectral emission per unit wavelength peaks at 4.0 μm. Use b = 2.90 × 10⁻³ m·K to estimate its temperature. If its peak later moves to 2.0 μm with the same emitting area, compare the total emitted powers.

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WORKED EXAMPLE

Combine spectral and area information

Two blackbody surfaces have equal total emitted powers. Surface B has twice the Kelvin temperature of surface A. What is A_B/A_A?

MEMBERSThe approach, step-by-step working and check are for members.Unlock →

Study with a tutor prompt

Copy this into your AI assistant, then describe where you got stuck. It asks the tutor to coach you one step at a time. Check its reasoning against the lesson.

Topic: Thermal radiation and the wavelength of a spectral peak
Focus: Infer temperature only after identifying the spectrum and units
Learning goals:
- Explain radiative transfer through vacuum and exchange at equilibrium.
- Distinguish blackbody, spectral and gray-body approximations.
- Use actual emitting area and Kelvin temperature in total power.
- Subtract surrounding radiation under a stated enclosure model.
- Balance projected absorption against whole-surface emission.
- Use wavelength-based Wien inference without confusing spectral representations.
- Derive the small-excess-temperature radiation limit.
Equations in this section (LaTeX):
Build the physical reasoning before choosing an equation.

Start by checking the prerequisite idea I need most. Use a simple example, then change one condition to test my understanding.

Back to chapter contents ↑

08 / Thermal radiation and the wavelength of a spectral peak

Newton cooling can emerge as a small-temperature-difference limit

Let T = T_a + θ with |θ| much smaller than the absolute ambient temperature. Expanding T⁴ gives T_a⁴ + 4T_a³θ plus terms quadratic and higher in θ. The net radiation is then approximately 4εσAT_a³θ.

For a body with uniform temperature and constant heat capacity C, the energy balance becomes C dθ/dt ≈ −4εσAT_a³θ. This has the exponential Newton-cooling form, with radiative rate coefficient 4εσAT_a³/C.

The small parameter is θ/T_a in Kelvin, not simply whether a Celsius number seems small. At large temperature differences, the neglected higher powers matter and a constant-coefficient exponential is no longer the exact radiation-only cooling law.

Convection may contribute another approximately linear loss over a limited range. In that case effective conductances add, but their constancy and the body’s nearly uniform temperature must still be checked. A successful exponential fit does not uniquely identify radiation as the only mechanism.

T^4-T_a^4\approx4T_a^3(T-T_a)\quad\text{when}\quad |T-T_a|\ll T_a

This approximation connects the radiation law to a linear loss model; all temperatures in the expansion are absolute.

STOP & THINK

Why can radiation sometimes be approximated by a Newton-cooling law?

The fourth power is always equal to a first power
Near ambient, the fourth-power difference has a leading term proportional to temperature excess
Radiation vanishes at room temperature

MEMBERSAnswer checking, feedback and the explanation are for members.Unlock →

Study with a tutor prompt

Copy this into your AI assistant, then describe where you got stuck. It asks the tutor to coach you one step at a time. Check its reasoning against the lesson.

Topic: Thermal radiation and the wavelength of a spectral peak
Focus: Newton cooling can emerge as a small-temperature-difference limit
Learning goals:
- Explain radiative transfer through vacuum and exchange at equilibrium.
- Distinguish blackbody, spectral and gray-body approximations.
- Use actual emitting area and Kelvin temperature in total power.
- Subtract surrounding radiation under a stated enclosure model.
- Balance projected absorption against whole-surface emission.
- Use wavelength-based Wien inference without confusing spectral representations.
- Derive the small-excess-temperature radiation limit.
Equations in this section (LaTeX):
T^4-T_a^4\approx4T_a^3(T-T_a)\quad\text{when}\quad |T-T_a|\ll T_a
Meaning: This approximation connects the radiation law to a linear loss model; all temperatures in the expansion are absolute.

Start by checking the prerequisite idea I need most. Use a simple example, then change one condition to test my understanding.

Back to chapter contents ↑

BRING THE IDEAS TOGETHER

What should stay with you

Finite-temperature bodies emit even at radiative equilibrium.
Emissivity and absorptivity comparisons must refer to the relevant spectra and conditions.
Emission scales as εAT⁴; net exchange also depends on incoming radiation.
Projected absorbing area can differ from emitting area.
Wien’s law describes the peak of a per-wavelength blackbody spectrum.
The wavelength peak is not the only emitted wavelength and does not directly convert to the frequency-density peak.
A small temperature excess can linearize a radiative loss law.

RETRIEVE, THEN EXPLAIN

Try it without the examples

Work these out before checking. If an answer surprises you, identify which assumption or step needs another look. A correct choice is most useful when you can explain why the alternatives fail.

SELF CHECK 1

A blackbody wavelength peak changes from 6 μm to 3 μm. What is the new-to-old absolute-temperature ratio?

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SELF CHECK 2

At fixed area and emissivity, absolute temperature increases by a factor of three. What is the emitted-power ratio?

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SELF CHECK 3

May εσAT⁴ alone be interpreted as net cooling power in a warm enclosure?

Yes, it already subtracts all absorption
No; incoming radiation and other transfers must be included
Only if T is in Celsius

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SELF CHECK 4

Does c divided by the wavelength-density peak always equal the frequency-density peak?

Yes, peaks transform without changing the density
No; changing the spectral variable changes the density weighting
Only for an ideal blackbody

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SELF CHECK 5

Does a surface looking black in visible light establish its thermal infrared emissivity?

Yes, visible appearance fixes every wavelength
No; the spectral response can differ
Yes, provided its area is known

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APPLY THE CHAPTER

Take the ideas into a problem

Try a complete problem next. Commit to a method before revealing a hint, then compare your reasoning with the worked solution.

The peak shifts as a body heatsIntermediate · Hints and guided reasoning A hotter surface radiates much moreIntermediate · Hints and guided reasoning Emission is not net coolingIntermediate · Hints and guided reasoning A smaller but hotter emitterIntermediate · Hints and guided reasoning

COME BACK TO THE IDEA

What can you explain later?

Try these from memory at your next study session, then again a few days later. Say your reasoning aloud or sketch it before looking. Adjust the gap to what you can explain.

Next study session

For the same ideal blackbody area, what happens to emitted power if absolute temperature doubles?

Compare your reasoning

It rises by a factor of sixteen because emitted power is proportional to T⁴. Net loss also depends on the surroundings, so it need not follow that same ratio.

Revisit the explanation →

A few days later: change the situation

A thermal spectrum’s wavelength peak moves to shorter wavelengths. What temperature change does the ideal blackbody model suggest, and what measurement distinction matters?

Compare your reasoning

It suggests a higher temperature. Specify a spectrum per unit wavelength: the peak of a spectrum per unit frequency is a different maximum and cannot be converted by simply taking c divided by the wavelength peak.

Revisit the explanation →

Compare the physical reason, the assumptions and the conclusion. Your wording can differ. If one part is missing, revisit that section and try explaining it again after a break.

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