IB Physics HL B.1 Thermal energy transfers Questions

SLSL HLHL

Explore how particle models explain temperature and internal energy, how thermal energy moves or changes state, and how radiation links to stellar brightness and temperature.

356 questions in this syllabus scope, with question parts counted together.

Exam points & syllabus

Exam points

Compare solids, liquids and gases through particle spacing, attraction and freedom of motion, distinguishing fixed neighbours from liquid rearrangement.
Use the cube root of a density ratio for particle-spacing estimates; a gas 1000 times less dense has spacing about 10 times greater.
Use ρ = m/V with the full geometric volume, or convert number density to mass density before finding total mass.
For swept material, use Δm = ρAvΔt or ṁ = ρAv; for immersed or floating objects, relate displaced volume to buoyancy and density.
Read water’s density maximum near 4°C and explain how floating, insulating ice helps liquid water remain below a frozen lake surface.
Keep temperature intervals unchanged between Celsius and kelvin; convert absolute Celsius temperatures before molecular or radiation calculations.
Use mean molecular KE = 3kBT/2 and distinguish equal energy per particle at the same temperature from equal whole-sample internal energy.
For thermal speed estimates, use vrms = √(3kBT/m) with single-particle mass; at equal T, speed ratios vary as 1/√m.
Check kB units as J/K and convert a given energy per particle from eV, MeV or TeV to joules before finding temperature.
Define internal energy as the total random molecular kinetic energy plus intermolecular potential energy; contrast this store with heat transfer.
In an ideal gas, neglect intermolecular potential energy; at a phase boundary, compare unchanged mean KE with changing PE and internal energy.
Explain constant-temperature melting or boiling using absorbed energy and increased intermolecular PE; reverse the energy and PE changes for freezing.
Distinguish boiling throughout a liquid from surface evaporation, and identify increased surface area as increasing evaporation at fixed temperature.
Use the stated initial phase and temperature when choosing a heating graph; a solid already at its melting point begins with a plateau.
Use a temperature difference to determine net transfer direction and explain why cooling slows as that difference shrinks.
Wait for thermal equilibrium with the surroundings before taking a pressure reading in a constant-temperature gas experiment.
Distinguish specific heat capacity, object thermal capacity C = mc, and specific latent heat for a constant-temperature phase change.
Use Q = mcΔT and Q = mL with consistent kg and joule units; divide by mc for a temperature rise or by L for the mass changing phase.
Add the separate warming, melting and further warming stages, using each phase’s c and the correct geometric mass.
Find common mixture temperature by equating energy lost and gained, weighting each temperature change by the relevant mass and c.
Include warming of melted ice in ice–water calorimetry, and include both condensation and cooling of condensate in steam calorimetry.
Use the mass actually evaporated in L = Pt/Δm, and distinguish the frozen mass Q/L from the liquid mass remaining.
For a steady heater flow, use P = ṁcΔT or ṁL, converting molar flow to kg/s and stating a consistent flow or power unit.
Find P from a sloping temperature segment and L from only the phase-change plateau duration; convert graph minutes to seconds.
At fixed mass and power, compare latent heats through plateau durations and specific heats through inverse temperature–time slopes.
Separate input power from the rate of thermal-energy gain to find losses, and apply a given system efficiency once in a heating calculation.
Use m/A = ρh for a lake column’s cooling and freezing energy per area; for draining ice at 0°C, use tmin = ρAdL/P.
Respect the stated model when estimating thermal outcomes, including impact energy used for melting or c read over a small temperature interval.
Explain an omitted calorimeter term from its initial temperature: a warm container supplies extra energy, so ignoring it underestimates fusion L.
Report a thermal measurement with its uncertainty rounded to one significant figure and the measured value rounded to the matching place.
Identify radiation as electromagnetic energy transfer; distinguish contact conduction from convection carried by moving fluid.
Explain solid conduction through kinetic-energy transfer between adjacent particles; in metals include moving electrons colliding with atoms or ions.
Trace radioactive-core energy from decay-product motion to thermal energy conducted through solid rock and ice towards the surface.
Explain convection through warmer, less dense fluid rising and cooler, denser fluid replacing it; apply the chain to air or stellar plasma.
For a hot rock resting on the Moon, retain ground-contact conduction and radiation while excluding atmospheric convection.
Choose an additional loss mechanism consistent with an energy budget already accounting for radiation, such as ocean-to-air conduction.
Calculate conductive power P = kAΔT/Δx or flux P/A = kΔT/Δx, using boundary temperatures, thickness in metres and the correct rate unit.
At fixed conductivity and boundary temperatures, doubling layer thickness halves both the temperature gradient and conductive flux.
State L = σAT⁴ using absolute temperature; distinguish total emission from flux σT⁴ and use 4πR² for a spherical emitting surface.
Compare stellar luminosities using radius squared and temperature to the fourth power; use a fourth root to recover an unknown temperature.
At equal luminosity, explain why a cooler star has greater emitting area, or use R ∝ T⁻² to compare radii.
Find radiative equilibrium by balancing absorbed and emitted power, using kelvin and the model’s stated emissivity, albedo or atmospheric return flux.
Distinguish local illumination from a global spherical average; use a 1/4 disc-to-sphere factor only when the input flux has not already been averaged.
Use log(L/R²) = 4log T + log(4πσ) to test the T⁴ exponent from a gradient and infer σ from the fitted intercept.
Relate luminosity to received brightness with b = L/(4πd²), converting solar units and distance units before calculating b, L or d.
Compare observed brightness using both luminosity and inverse-square distance; for binary members at the same distance, b ratios equal L ratios.
Derive solar received flux from the source’s radiated power spreading over 4πd²; use the solar constant to reverse the calculation for luminosity.
Use supplied calibration graphs before an inverse-square distance calculation, and explain how uncorrected absorption causes distance overestimation.
For a covered point source, use distance C + x; infer C from the linearized intercepts and P = 4π/K² from the SI gradient of 1/√I against x.
Infer temperature from a black-body continuum maximum using λmaxT = 2.9 × 10⁻³ m K, converting nm, μm or mm to metres.
Use inverse peak-wavelength ratios to compare temperatures, and choose a reciprocal decreasing graph of λmax against absolute T.
Sketch an asymmetric black-body continuum with the correct peak; preserve a specified normalized height and shift a cooler spectrum towards longer λ.
Distinguish peak position from emission strength: equal peak wavelengths imply equal T, while different emission at equal area can indicate different e.
Outline the spectral temperature method by obtaining the spectrum, measuring its continuum maximum and applying Wien’s law; classify the resulting EM region.

Covered syllabus points

B.1.1—Molecular states B.1.2—Density B.1.3—Temperature scales B.1.4—Temperature scale changes B.1.5—Kelvin temperature and kinetic energy B.1.6—Internal energy B.1.7—Thermal transfer direction B.1.8—Phase change B.1.9—Specific heat and latent heat B.1.10—Thermal transfer mechanisms B.1.11—Conduction B.1.12—Conduction rate B.1.13—Convection B.1.14—Black-body radiation B.1.15—Apparent brightness B.1.16—Luminosity and brightness B.1.17—Wien’s displacement law

Exam points

Contrast fixed nearest-neighbour positions in a solid with molecules exchanging positions as liquid attractions break and re-form.
Explain most solids’ greater density through closer particle spacing, smaller volume and the same mass in that volume.
Use the cube root of a density ratio to estimate molecular spacing: a gas 1000 times less dense than its liquid has spacing about 10d.
Compare gas and solid particles by intermolecular distance, attraction and freedom of motion, stating the contrast explicitly.
At the same temperature, gas and solid particles have the same average kinetic energy in the molecular model, despite their different spacing.

[Maximum number: 3]

Ceres is a dwarf planet in the asteroid belt. The following data are available.

\begin{array}{ll} \text { Mean distance of Ceres from the Sun } & =4.4 \times 10^{11} \mathrm{~m} \\ \text { Mean power output of the Sun } & =3.8 \times 10^{26} \mathrm{~W} \end{array}

At low temperatures such as the mean temperature of Ceres, water undergoes a phase change directly from solid to gas.

Compare the molecular conditions of the solid phase and the gas phase at the same temperature.

Exam points

Infer liquid density from the loss in apparent mass on immersion: ρ = (m_air − m_immersed)/V, converting grams to kilograms.
Convert number density to mass density using particle mass, then multiply by the full spherical volume; show numerical substitution for a given target.
Use swept cylindrical volume to obtain collected mass: Δm = ρAvΔt, or mass flow rate ṁ = ρAv.
For a floating cylindrical iceberg, use the submerged fraction ρ_ice/ρ_water to recover total height before calculating m = ρ_iceAH.
Read water’s maximum density from the enlarged temperature graph: about 4°C, equivalent to 277 K when the unit is stated.
Explain how lower-density ice remains on the surface and insulates liquid water below, helping prevent a lake from freezing completely.

[Maximum number: 1]

A cylindrical spacecraft of cross-sectional area S moves with velocity v. The spacecraft enters a region of dust of density $\rho$ . All the dust that comes into contact with the forward cross-sectional area of the spacecraft sticks to the spacecraft increasing its mass.

Show that in time $\Delta t$ the mass of the spacecraft will increase by an amount $\rho \operatorname{Sv} \Delta t$ .

Identifies length of cylinder as $v \Delta t$ so volume as $S \times v \times \Delta t$ to show the result

Exam points

Calculate ΔT = 273 − (−153) = 426°C = 426 K; do not add 273 when converting a temperature difference.

[Maximum number: 1]

The temperature of an object is $-153^{\circ} \mathrm{C}$ . Its temperature is raised to $273^{\circ} \mathrm{C}$ . What is the temperature change of the object?

699 K

426 K

153 K

120 K

Exam points

Use average particle kinetic energy proportional to absolute temperature, Ek = 3kBT/2; energy is not numerically equal to T.
At a common temperature, compare equal average kinetic energy per particle across species or phases; this does not imply equal whole-sample energy.
For ideal gases at the same temperature, use a thermal-speed ratio proportional to 1/√m; mass ratios 2 and 8 give factors 1/√2 and √8.
Use vrms = √(3kBT/m) for RMS or accepted thermal-speed estimates, converting molar mass to a single-particle mass in kilograms.
Identify kB units as J/K and kB = R/NA; rearranging Ek = 3kBT/2 gives kB = 2Ek/(3T), not Ek/T.
Convert Celsius to Kelvin before calculating average molecular KE: −38°C becomes 235 K and gives about 4.9 × 10⁻²¹ J.
Convert a supplied energy per particle from eV, MeV or TeV to joules before using T = 2Ek/(3kB).
Explain warming milk through increased average molecular KE and a higher average molecular speed, linking both changes to temperature.

[Maximum number: 1]

Ceres is a dwarf planet in the asteroid belt. The following data are available.

\begin{array}{ll} \text { Mean distance of Ceres from the Sun } & =4.4 \times 10^{11} \mathrm{~m} \\ \text { Mean power output of the Sun } & =3.8 \times 10^{26} \mathrm{~W} \end{array}

At low temperatures such as the mean temperature of Ceres, water undergoes a phase change directly from solid to gas.

The maximum surface temperature of Ceres is $-38^{\circ} \mathrm{C}$ . Observations show that significant quantities of water vapour are released from the surface of Ceres every second when the temperature is at this maximum. Calculate the mean kinetic energy of a molecule of water vapour at this temperature.

4.9\times10^{-21}\,\mathrm{J}

Exam points

Define internal energy as the total random kinetic energy and intermolecular potential energy of the particles, rather than a sum of per-particle averages.
Distinguish internal energy, a total particle-energy store, from temperature, which measures average particle kinetic energy.
Distinguish internal energy from heat: heat is energy transferred between bodies because of a temperature difference.
In the ideal-gas approximation, neglect intermolecular potential energy; real-gas internal energy can include intermolecular interactions.
For equal amounts at the same phase-change temperature, compare unchanged average KE with higher PE in liquid or gas; freezing lowers PE and internal energy.
On a melting temperature plateau, explain why later internal energy is greater even though temperature and average molecular KE are unchanged.
Estimate a liquid’s internal-energy change from its measured temperature rise: 0.25 × 4200 × 27 = 2.835 × 10⁴ J for the water.
In the elementary phase-motion model, rank the vibrational contribution as solid > liquid > gas; this is a qualitative model comparison.

[Maximum number: 2]

This question is in two parts. Part 1 is about gravitational force fields. Part 2 is about properties of a gas.

With respect to a gas, explain the meaning of the terms thermal energy and internal energy.

Thermal energy:

Internal energy:

Exam points

After changing a trapped gas’s volume, wait for thermal equilibrium with the surroundings before measuring pressure in a constant-temperature investigation.
Distinguish heat, transferred energy measured in joules, from temperature, which determines transfer direction and is measured in kelvin.
Explain a cooling curve’s decreasing |dT/dt| through the shrinking temperature difference between the room and its surroundings.

[Maximum number: 1]

The equipment shown in the diagram was used by a student to investigate the variation with volume, of the pressure p of air, at constant temperature. The air was trapped in a tube of constant cross-sectional area above a column of oil.

The pump forces oil to move up the tube decreasing the volume of the trapped air.

The student measured the height H of the air column and the corresponding air pressure p. After each reduction in the volume the student waited for some time before measuring the pressure. Outline why this was necessary.

Exam points

Distinguish boiling throughout a liquid from evaporation at its surface.
At a fixed temperature, identify increased liquid surface area as a change that increases the evaporation rate.
For a solid already at its melting point, choose a T–E graph with an initial plateau followed by a temperature rise after melting finishes.
Explain melting or boiling at constant temperature through increased intermolecular potential energy or separation, while average molecular KE is unchanged.
During freezing, intermolecular bonds form and release energy; potential energy falls while average random molecular KE and temperature stay constant.

[Maximum number: 3]

This question is in two parts. Part 1 is about thermal properties of matter. Part 2 is about quantum physics.

Part 1 Thermal properties of matter

Explain, in terms of the energy of its molecules, why the temperature of a pure substance does not change during melting.

Exam points

Define specific heat capacity per unit mass and per kelvin; distinguish it from an object’s thermal capacity C = mc.
Define specific latent heat of fusion as energy per unit mass for melting or freezing at constant temperature.
Rearrange Q = mcΔT or Q = mL with consistent kg, joule and temperature-interval units; omit warming when already at the melting point.
Split a thermal process into warming, phase change and further warming, using each phase’s c and adding mL only during the phase change.
For an isolated mixture, equate energy lost and gained using each mass, specific heat and temperature change to find the common temperature.
When ice melts in warm water, include both fusion energy and the energy needed to warm the melted water to the final temperature.
In steam calorimetry, use the mass gain and include both condensation energy and the cooling of the condensate to the final temperature.
Use the evaporated mass decrease, rather than the water or kettle mass remaining, in L = Pt/Δm.
For a steady flow, use P = ṁcΔT for heating or P = ṁL for vaporization, converting molar flow to mass flow when needed.
Use a rising or falling temperature segment to find P = mcΔT/Δt, and convert graph times from minutes to seconds.
Use only the phase-change plateau duration in L = PΔt/m or P = mL/Δt; exclude adjacent warming or cooling intervals.
At fixed mass and power, compare latent heats using plateau durations and specific heats using inverse temperature–time slopes.
Obtain L/c from a constant-power heating graph by combining a plateau duration with the temperature change and duration of a sloping segment.
Find heating losses from Pinput − mcΔT/Δt, and include the stated system efficiency when matching solar input to a water temperature rise.
Use density and the stated geometry to find thermal mass; for a lake column per unit area, use m/A = ρh before adding cooling and freezing energy.
For ice already at 0°C that drains away as it melts, calculate tmin = ρAdL/P from the cleared area and ice-layer thickness.
After a freezing interval, use Δm = Q/L for the mass frozen and subtract it from the initial mass if the question asks for liquid remaining.
Use the stated energy-transfer model to find the melted fraction from impact energy per kilogram divided by the specific latent heat.
When a specific heat graph varies over a small temperature interval, estimate c over that interval and keep its kJ or J scale consistent.
Combine ΔT = Q/(mc) with geometric mass scaling: doubling a cube’s side multiplies its mass by eight.
Explain an omitted container term using its initial temperature and energy transfer; an initially warm container makes the inferred fusion L too small.

[Maximum number: 2]

The graph shows the variation with time of the height of the International Space Station (ISS) during a 30-day period.

The following data are available:

\begin{aligned} \text { Mass of Earth } & =5.98 \times 10^{24} \mathrm{~kg} \\ \text { Mass of the ISS } & =4.20 \times 10^{5} \mathrm{~kg} \\ \text { Radius of the Earth } & =6.38 \times 10^{6} \mathrm{~m} \end{aligned}

For the 30-day period indicated in the graph the loss of total energy of the ISS is $4.5 \times 10^{9} \mathrm{~J}$ .

Estimate the increase in the temperature of the ISS assuming all the lost energy went into thermal energy of the ISS. Take the specific heat capacity of the ISS to be $500 \mathrm{Jkg}^{-1} \mathrm{~K}^{-1}$ .

$\begin{aligned} \Delta T=\frac{Q}{m c} \quad \Delta T=\text { « } \frac{4.5 \times 10^{9}}{4.2 \times 10^{5} \times 500}=\gg 21 \mathrm{~K} \text { OR } 21^{\circ} \mathrm{C} \quad \end{aligned}$

Award [2] if 21 is seen as the answer without working

Exam points

Define thermal radiation as the emission and transfer of energy by electromagnetic waves.
Identify conduction through contact or convection by air currents, and state the transfer direction from the warmer surroundings to colder ice.
Explain convection around a hot pipe: nearby air warms, becomes less dense and rises, with cooler air replacing it.
For a hot object resting on the Moon, retain conduction to the ground and radiation; exclude convection because there is no surrounding atmosphere.
When an energy budget already includes thermal radiation, identify an additional allowed loss mechanism, such as conduction from ocean water to air.

[Maximum number: 3]

The radioactive nuclide beryllium-10 (Be-10) undergoes beta minus ( $\beta$ -) decay to form a stable boron (B) nuclide.

(a)

An ice sample is moved to a laboratory for analysis. The temperature of the sample is $-20^{\circ} \mathrm{C}$ .

[ 3 ]

(i)

State what is meant by thermal radiation.

[ 1 ]

(ii)

The temperature in the laboratory is higher than the temperature of the ice sample. Describe one other energy transfer that occurs between the ice sample and the laboratory.

[ 2 ]

Exam points

Identify conduction as the mechanism transferring thermal energy through a solid metal wall.
Explain conduction through particle vibrations and the transfer of kinetic energy to adjacent particles through interactions or collisions.
In a metal, explain the contribution of moving electrons that transfer energy through collisions with atoms or ions.
For a radioactive rocky core beneath solid ice, link decay-product kinetic energy to thermal energy that reaches the surface mainly by conduction.

[Maximum number: 2]

Describe the mechanism of heat transfer by conduction.

The diagram shows a wall separating the inside of a room from the outside. The temperature of the room is kept constant by a heater.

Exam points

Calculate conduction power with P = kAΔT/Δx, using the wall’s area and thickness and giving the result in watts.
For conduction rate per unit area, use P/A = kΔT/Δx; convert ice thickness to metres and use the temperature difference across the layer.
At fixed boundary temperatures and conductivity, increasing thickness reduces the temperature gradient and conductive flux in inverse proportion.

[Maximum number: 2]

The following data are available:

\begin{aligned} \text { Thickness of wall } & =0.25 \mathrm{~m} \\ \text { Area of wall } & =18 \mathrm{~m}^{2} \\ \text { Thermal conductivity of wall } & =1.3 \mathrm{Wm}^{-1} \mathrm{~K}^{-1} \\ \text { Constant room temperature } & =22^{\circ} \mathrm{C} \\ \text { Constant outside temperature } & =13^{\circ} \mathrm{C} \end{aligned}

Estimate the rate at which thermal energy leaves the room through the wall giving the answer with an appropriate unit.

$\text { « } \frac{\Delta Q}{\Delta t}=k A \frac{\Delta T}{\Delta x}=\frac{1.3 \times 18 \times(22-13)}{0.25} \text { » } 8.4 \times 10^{2} \quad$

Unit is $\mathrm{W} / \mathrm{Js}^{-1} / \mathrm{kgm}^{2} \mathrm{~s}^{-3}$

Ignore the sign in MP1

Exam points

Explain stellar convection using temperature and density differences: warmer, less dense plasma rises, while cooler, denser plasma sinks.

[Maximum number: 2]

Star A is a main sequence star.

The data for Star A and the Sun are given in a table.

Outline why regions of convection form in Star A.

Exam points

State the Stefan–Boltzmann law L = σAT⁴ with symbols defined: emitted power depends on area and the fourth power of absolute temperature.
Distinguish total emitted power L = σAT⁴ from emitted power per unit surface area σT⁴.
For a spherical emitter, use A = 4πR² and convert kilometres to metres before calculating luminosity.
Compare luminosities using L₁/L₂ = (R₁/R₂)²(T₁/T₂)⁴ for black bodies or bodies with the same emissivity.
At equal luminosity, use R ∝ T⁻² to compare radii, or explain why the cooler star on an HR diagram must have a larger surface area.
Rearrange a luminosity ratio with the two radius values to determine an unknown stellar surface temperature using a fourth root.
Balance absorbed and emitted power to find equilibrium temperature; take the fourth root and use kelvin in the radiation equation.
For a whole spherical planet, average incident solar flux over its surface using the disc-to-sphere area ratio 1/4 before finding temperature.
Distinguish a local illuminated-surface temperature from a global average; lower incident power per area gives a lower equilibrium temperature.
Use the given emissivity with the Stefan–Boltzmann reference power and apply albedo to absorbed solar flux when the model specifies it.
For a surface receiving atmospheric back-radiation, include both absorbed sunlight and returned infrared energy in the equilibrium balance.
Combine L = σAT⁴ with b = L/(4πd²) to show that thermal-source apparent brightness is proportional to AT⁴/d².
Apply a star’s thermal-emission brightness model to its own light; explain why reflected sunlight controls a bright planet’s visible appearance.
On a graph of log(L/R²) against log T, derive a gradient of 4 and compare it with the measured gradient when testing the radiation law.
Obtain σ from the log–log intercept c using σ = 10ᶜ/(4π), showing the working rather than treating the intercept as the constant.
At equal emissivity, compare emitted surface intensities using I ∝ T⁴; use temperature ratios rather than Celsius differences.

[Maximum number: 1]

Star A is a main sequence star.

The data for Star A and the Sun are given in a table.

Show that the luminosity of Star A is about half that of the Sun.

$\frac{L_{A}}{L_{S}}=\left(\frac{0.9 R_{s}}{R_{s}}\right)^{2}\left(\frac{5200}{5800}\right)^{4}=0.52$

Must see full substitution OR answer to 2 (or more) significant figures.

Allow the reverse fraction, leading to 1.92.

Exam points

When comparing an unresolved binary system with a single star, include the observed brightness contributed by both members of the binary.

[Maximum number: 1]

Alpha Centauri A and B form the closest binary star system to the Earth. This binary star system is the third brightest stellar object in the night sky.

Arcturus is the fourth brightest star in the night sky. Its apparent brightness is slightly greater than that of the star Alpha Centauri A.

Outline why the binary star system Alpha Centauri appears brighter than Arcturus.

Exam points

Distinguish luminosity, the total power emitted by a source, from apparent brightness, the power received per unit area.
Use b = L/(4πd²) with the distance from the source to the observer; rearrange to find b, L or d and include the square root for distance.
Convert luminosities given in solar units to watts, and convert distances between metres and parsecs when required.
At fixed source luminosity, compare received intensities using the inverse square of the source distances.
For two sources, compare b₁/b₂ = (L₁/L₂)(d₂/d₁)²; a more luminous source can appear fainter if it is farther away.
For binary stars at approximately the same distance, state that common distance before equating their brightness ratio to their luminosity ratio.
Use the Sun’s reference distance of 1 AU when comparing a star’s luminosity and apparent brightness with solar values to infer its distance.
Derive received stellar flux by dividing L = 4πR²σT⁴ by 4πd², distinguishing the source radius R from the observer distance d.
Infer the Sun’s luminosity from the solar constant using L = 4πd²S, with d equal to the Earth–Sun distance.
Apply a stated reflected fraction after inverse-square dilution when finding the solar intensity reaching a surface.
When calibration graphs are supplied, read the required period and luminosity from them before applying d = √(L/(4πb)).
Explain how unaccounted light absorption lowers measured b and therefore makes the inferred distance too large at a fixed luminosity.
For a covered point source, use d = C + x; on a graph of 1/√I against x, find the positive cover radius from −xintercept or yintercept/gradient.
From the gradient K of 1/√I against distance in metres, determine P = 4π/K²; use widely separated line points and give power in watts.

[Maximum number: 2]

The diagram shows a simplified energy-balance model for the Earth surface-atmosphere system.

The following data are given:

\begin{aligned} \text { Average albedo of Earth } & =0.30 \\ \text { Average global temperature of the surface } & =288 \mathrm{~K} \\ \text { Average Earth-Sun distance } & =1.5 \times 10^{11} \mathrm{~m} \end{aligned}

Show, with reference to the solar constant, that the total power radiated by the Sun is about $4 \times 10^{26} \mathrm{~W}$ .

Recognition that $r=1.5 \times 10^{11} m$ AND $S=1.36 \times 10^{3} \mathrm{~W} \mathrm{~m}^{-2}$ $4 \pi\left(1.5 \times 10^{11}\right)^{2} \times 1.36 \times 10^{3}$ or $3.8 \times 10^{26} \mathrm{~W}$

Unit is not required.

The values of r and S must be seen to award MP1.

Marking guidance:

Allow ECF from use of
$S=1.4 \times 10^{3} \mathrm{Wm}^{-2}$

Exam points

Use λmaxT = 2.9 × 10⁻³ m K to find temperature or peak wavelength, converting nm, μm or mm to metres.
Use the correct emitting object’s peak wavelength and absolute temperature; convert Celsius to kelvin before applying Wien’s law.
Read the wavelength at the maximum of a continuous black-body spectrum, then use Wien’s law to infer the temperature.
Use T₁/T₂ = λmax,₂/λmax,₁ to compare temperatures; compare peak positions rather than peak heights.
Predict peak shifts using λmax ∝ 1/T: doubling T halves λmax, while a 33% rise in T reduces λmax to about 3/4 of its initial value.
Choose a reciprocal decreasing curve for peak wavelength plotted against absolute temperature.
Sketch a continuous, asymmetric black-body spectrum with its maximum at the wavelength found from Wien’s law.
When spectra are normalized to the same maximum intensity, preserve that peak height while moving a cooler body’s maximum to a longer wavelength.
After calculating a peak wavelength, identify its region of the electromagnetic spectrum.
For a show-that result, display the full substitution or enough significant figures to establish the stated approximate value.

[Maximum number: 1]

Star A is a main sequence star.

The data for Star A and the Sun are given in a table.

Show that the peak wavelength emitted from Star A is about 560 nm .

$\lambda_{\text {max }}=\frac{2.9 \times 10^{-3}}{5200}=5.58 \times 10^{-7} \mathrm{~m}$ OR $558 \mathrm{~nm}$

Must see full substitution OR answer to 3 (or more) significant
figures.

More syllabus points

B.1.3—Temperature scales2 questions

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