IB Physics SL 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.

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

Exam points & syllabus

Exam points

Explain phase behaviour through particle motion and intermolecular interactions, while distinguishing mean kinetic energy from total internal energy.
Use density with the actual mass and volume change; retain water’s density anomaly when explaining surface ice and insulation.
Convert absolute temperature with the Celsius offset, but calculate a temperature change by subtraction without adding 273.
Use kelvin temperature for mean particle kinetic energy and thermal-speed ratios; equal-temperature gases have equal mean energy, not equal speeds.
Define internal energy as the total random kinetic and intermolecular potential energies; heat is energy transferred because of a temperature difference.
Use temperature difference to determine net spontaneous thermal-transfer direction; equal temperatures give no net transfer between bodies in contact.
On a phase-change plateau, constant temperature means constant mean kinetic energy; potential energy and internal energy may still change.
Distinguish evaporation at a liquid surface from boiling throughout the liquid; explain changes in rate using the stated physical change.
Choose Q = mcΔT or Q = mL for each stage, and include every warming, cooling or phase-change term in one consistent energy balance.
Relate heater power to the correct rate: mc(dT/dt) on a temperature ramp, L(dm/dt) during vaporisation, or ṁcΔT in continuous flow.
Read heating-graph intervals and slopes for the requested process; use only the plateau duration for latent energy.
In insulated mixing, equate energy lost and gained using each body’s own temperature change to the common final temperature.
Account for heater input, stored-energy increase and losses separately; a powered steady state balances rates without equal surrounding temperature.
Explain experimental bias through the affected measured or lost-energy term before stating whether the inferred thermal property is too large or small.
Connect supplied mechanical or electrical input to thermal gain with the correct heated mass, time interval and conversion fraction.
Explain conduction, convection and radiation with their distinct mechanisms; trapped-air insulation reduces both conduction and bulk circulation.
For conduction rate use P = kAΔT/Δx, distinguish total power from heat flux, and convert layer thickness and geometry consistently.
Use the Stefan–Boltzmann law with kelvin temperature, distinguishing total emitted power from emitted power per unit area.
Compare stellar luminosity with radius squared and temperature to the fourth power; invert the ratio consistently when solving for radius or temperature.
Build radiative equilibrium from absorbed and emitted power with the stated geometry, reflection and atmospheric contributions.
Distinguish observed brightness from intrinsic luminosity, and include both stellar contributions for an unresolved binary.
Use b = L/(4πd²) for flux, luminosity or distance, retaining solar multipliers and converting astronomical units for absolute SI calculations.
Justify observed-brightness comparisons with both luminosity and distance; cancel distance only for approximately equidistant sources.
Treat attenuated brightness as a source of distance bias: at the adopted luminosity, a lower observed flux implies an overestimated distance.
Infer temperature from the continuum spectral maximum with Wien’s law; distinguish the body’s own emission peak from incident light or a spectral line.
Sketch asymmetric black-body spectra and apply the inverse peak-temperature relation, respecting any independently normalised curve heights.
Use graph transformations to identify radiation-law parameters: the log(L/R²) slope gives the temperature exponent and the intercept gives 4πσ.

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 vibration about fixed mean positions in a solid with particles moving relative to neighbours in a liquid; name the microscopic difference.
Discuss intermolecular interactions rather than breaking molecules apart: a liquid can break and re-form attractions as neighbours change.
For most substances, closer particle spacing gives the same mass a smaller volume and therefore a higher solid density; retain the water exception.
At the same temperature, compare gas and solid spacing, interactions and freedom of motion while keeping their mean random kinetic energy the same.

[Maximum number: 2]

A cylindrical cork of height H and cross-sectional area A is floating stationary in water. Its depth below the water surface is D.

Explain why the density of most substances in a solid state is larger than its density in a liquid state.

Water shows an anomaly with respect to what is stated in (c)(i).
Graph 1 shows the variation with temperature of the density of water between $-100^{\circ} \mathrm{C}$ and $100^{\circ} \mathrm{C}$ . Graph 2 shows the same graph enlarged for the range 0 to $10^{\circ} \mathrm{C}$ .

Exam points

For a fixed mass that expands, explain the density decrease with both parts of ρ = m/V: volume increases while mass stays constant.
Use m = ρAΔh for water released from a basin; the volume uses the full level change, without the half-height factor used in a later energy calculation.
With a supplied buoyancy relation, infer liquid density from the apparent-mass difference divided by displaced volume; convert grams to kilograms.
Link water’s density anomaly to surface ice and denser liquid below, then explain how the ice insulates water and limits complete freezing.

[Maximum number: 2]

This question is about a tidal power station.

A tidal power station is built for a coastal town. Sea water is stored in a tidal basin behind a dam at high tide and released in a controlled manner between high tides, so that it passes through turbines to generate electricity.

The following data are available.

Show that the mass of sea water released between successive high and low tides is about $2.8 \times 10^{8} \mathrm{~kg}$ .

$m=\rho \Delta V=\rho A \Delta h$ ;

\begin{aligned} & =1.1 \times 10^{3} \times 1.4 \times 10^{5} \times 1.8 ; \\ & \left(\approx 2.8 \times 10^{8} \mathrm{~kg}\right) \end{aligned}

Exam points

Convert a Celsius temperature to kelvin by adding approximately 273; 57 °C corresponds to 330 K.
Keep the sign of the Celsius value when adding the offset: −100 °C corresponds to 173 K, a positive absolute temperature.

[Maximum number: 1]

Which of the following is equivalent to a temperature of $-100^{\circ} \mathrm{C}$ ?

-373 K

-173 K

173 K

$373 \mathrm{~K}$

Exam points

A temperature change has the same numerical value in kelvin and degrees Celsius; subtract final minus initial without adding or subtracting 273.
Retain the sign of a negative starting temperature: from −153 °C to 273 °C the increase is 273 − (−153) = 426 K.
Equal temperature increases on the two scales do not imply equal heating energies for different systems when mass and heat capacity are unknown.

[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 mean particle kinetic energy 3kBT/2 with the final absolute temperature; include a stated temperature increase before substituting.
For gases sharing an equilibrium temperature, mean translational kinetic energy per particle is equal regardless of molecular mass or concentration.
Compare mean kinetic energies using kelvin-temperature ratios, without multiplying by the amount of gas, volume or molecular mass.
For the same ideal gas, thermal speed scales as √T; at equal temperature, the speed ratio for different molecular masses scales as 1/√m.
Link temperature to average random particle kinetic energy, not bulk motion or the full sum of random kinetic and intermolecular potential energies.
In rapid piston compression, explain the temperature rise through molecules gaining speed on collision with the moving piston.

[Maximum number: 2]

A mass of 1.0 kg of water is brought to its boiling point of $100^{\circ} \mathrm{C}$ using an electric heater of power 1.6 kW .

The molar mass of water is $18 \mathrm{~g} \mathrm{~mol}^{-1}$ . Estimate the average speed of the water molecules in the vapor produced. Assume the vapor behaves as an ideal gas.

$E_k=\frac32(1.38\times10^{-23})(373)=7.7\times10^{-21}\ \mathrm{J}$ .
$v=\sqrt{\frac{3\times1.38\times10^{-23}\times6.02\times10^{23}\times373}{0.018}}=720\ \mathrm{m\ s^{-1}}$ .

v=\sqrt{\frac{3(1.38\times10^{-23})(6.02\times10^{23})(373)}{0.018}}=720\ \mathrm{m\ s^{-1}}

Exam points

Define internal energy as the total random kinetic energy plus intermolecular potential energy of all the particles, not a sum of mean energies.
Distinguish total internal energy from temperature, which measures average random particle kinetic energy; mention the particles in both descriptions.
Distinguish internal energy stored in a substance from heat, which is energy transferred because of a temperature difference.
At the same temperature and particle amount, explain phase internal-energy differences through potential energy while mean random kinetic energy stays equal.
On a melting plateau, internal energy can increase at constant temperature as intermolecular potential energy increases.
For constant-temperature sublimation, internal energy and intermolecular potential energy increase; for freezing, both decrease.
In the isolated water-and-ice model, internal transfers or melting can redistribute energy while the total internal energy of the system stays constant.
Friction can transfer gravitational or other mechanical energy into a body’s internal energy even when its macroscopic speed is constant.

[Maximum number: 2]

Distinguish between internal energy and thermal energy (heat).

Internal energy:
Thermal energy:

Exam points

Use the temperature difference to identify the net direction of spontaneous thermal transfer; temperatures alone do not specify stored energy or mechanism.
No net thermal transfer between bodies in contact requires equal temperatures, not equal masses or thermal capacities.
Distinguish heat as energy transferred from temperature as a particle-energy measure and indicator of flow direction; use J for heat and K for temperature.
In an uninsulated heating experiment, heat enters while the sample is colder than its surroundings and leaves while it is hotter; assess the net balance.

[Maximum number: 3]

This question is in two parts. Part 1 is about the motion of a ship. Part 2 is about melting ice.

The whole of the experiment in (f)(i) and (f)(ii) is repeated with a container of negligible mass that is not isolated from the surroundings. The temperature of the surroundings is $18^{\circ} \mathrm{C}$ . Comment on the final temperature of the water in (f)(ii).

ice/water spends more time below $18^{\circ} \mathrm{C}$ ;
so net energy transfer is in to the system;
so final water temperature is higher;
or
ice/water spends less time below $18^{\circ} \mathrm{C}$ ;
so net energy transfer is out of the system;
so final water temperature is lower;

Exam points

During melting or boiling at constant temperature, supplied energy increases intermolecular potential energy while mean random kinetic energy stays unchanged.
During freezing, intermolecular interactions form and potential energy decreases; released energy allows the phase change while mean kinetic energy stays fixed.
A phase-change plateau in an insulated, powered sample does not mean constant internal energy or input balanced by external heat loss.
When freezing starts at the freezing point, the temperature-versus-energy-removed graph is horizontal throughout the phase change.
During vaporisation at the same temperature, molecular spacing and intermolecular potential energy increase while the same gas particles’ RMS speed stays fixed.
Evaporation occurs at a liquid’s surface across its liquid-temperature range; boiling occurs throughout the liquid at the boiling point for the stated pressure.
At constant temperature, increasing exposed liquid surface area increases the evaporation rate; a decrease in liquid volume alone is not the stated cause.
Describe melting through vibration about fixed positions, overcoming intermolecular attractions and gaining freedom to change neighbours or positions.

[Maximum number: 3]

The water in (b) is further heated until it starts to boil at constant temperature. It is boiled for 500 s measured from the time that it first starts to boil. The mass of water remaining after this time is 0.20 kg .

Explain, in terms of the energy of the molecules of the water, why the water boils at constant temperature.

Exam points

Distinguish specific heat capacity, whole-body thermal capacity and specific latent heat by unit mass, temperature interval and whether phase changes.
Use Q = mcΔT for sensible heating and Q = mL for phase change; split a process into separate stages when both occur.
Convert grams, kJ, minutes and millikelvin rates before combining them; temperature differences do not take an extra 273 offset.
For constant-power temperature ramps, use P = mc(dT/dt); at fixed mass and power, a steeper temperature slope means smaller specific heat capacity.
At fixed mass and power, compare latent heats through plateau durations; a longer plateau requires more latent energy.
Measure only the phase-change interval when inferring L = PΔt/m; subtract the plateau’s start time from its end time.
For an already-boiling liquid, increased heating power increases the vaporisation rate rather than temperature; use P = L(dm/dt).
For continuously flowing liquid, use P = ṁcΔT to find flow rate or temperature rise, and state a matching mass-per-time unit.
In insulated mixing, equate energy lost and gained using each body’s mass, heat capacity and own temperature change to the common final temperature.
When ice melts in warm water, include both fusion and subsequent warming of the meltwater; the original warm water cools to the same final temperature.
Subtract phase-change energy from the available heater energy before calculating a later temperature rise; retain the stated start of the new interval.
Use the relevant mass difference or phase fraction: distinguish mass vaporised, mass remaining, mass melted and total mass in the apparatus.
Connect a mechanical or electrical energy input to the thermal gain with the stated fraction and the correct heated mass.
Subtract energy retained in the sample from total input to find losses; at boiling the sample’s useful energy gain is mL.
Explain a bias through the affected energy term before stating overestimate or underestimate; different latent-heat methods can give opposite biases.
Use paired trials to remove a fixed container contribution, and distinguish an equilibrium result from a change in heat-transfer rate.
Use dimensionally correct ratios to eliminate unknown mass or heater power; retain units when comparing L/c or c/L.
For a steady heated block, infer heat loss at the same temperature from the initial cooling rate after switch-off; convert K/min to K/s.
For a minimum melting time from geometry, find mass = density × cleared area × thickness, then divide mL by useful heating power.
For a show-that result, provide the full balance, substitution or extra precision required by the scheme rather than repeating the rounded target.
Use the measured or graph-based specific heat value appropriate to the task; do not replace an experimental result with a remembered accepted value.
For water, justify Lv > Lf through the greater intermolecular energy change needed for vaporisation rather than only quoting the ranking.

[Maximum number: 3]

This question is in two parts. Part 1 is about ideal gases and specific heat capacity. Part 2 is about simple harmonic motion and waves.
Part 1 Ideal gases and specific heat capacity

Argon behaves as an ideal gas for a large range of temperatures and pressures. One mole of argon is confined in a cylinder by a freely moving piston.

The temperature of the argon is 300 K . The piston is fixed and the argon is heated at constant volume such that its internal energy increases by 620 J . The temperature of the argon is now 350 K .

Determine the specific heat capacity of argon in $\mathrm{Jkg}^{-1} \mathrm{~K}^{-1}$ under the condition of constant volume. (The molecular weight of argon is 40 )

Mass of gas $=0.040\ \mathrm{kg}$ .
$c=Q/(m\Delta T)$ , or $620=0.040\times c\times50$ .
$c=310\ \mathrm{J\ kg^{-1}\ K^{-1}}$ .

c=\frac{620}{0.040\times50}=310\ \mathrm{J\ kg^{-1}\ K^{-1}}

Exam points

Define thermal radiation as emission of electromagnetic energy or waves; infrared is the accepted example in the ice-sample context.
Explain trapped-air insulation with both mechanisms: air conducts poorly, and restricting its motion suppresses convection.
Relate heater placement to path thickness: a resistor near the upper surface transfers energy more readily through the thinner top layer.
For a solid rocky core and solid ice covering, trace decay-product kinetic energy into thermal energy, then identify conduction towards the surface.

[Maximum number: 3]

An electrically heated pad is designed to keep a pet warm.

The pad is heated using a resistor that is placed inside the pad. The dimensions of the resistor are shown on the diagram. The resistor has a resistance of $4.2 \Omega$ and a total length of 1.25 m .

When there is a current in the resistor, the temperature in the pad changes from a room temperature of $20^{\circ} \mathrm{C}$ to its operating temperature at $35^{\circ} \mathrm{C}$ .

The design of the pad encloses the resistor in a material that traps air. The design also places the resistor close to the top surface of the pad.

Explain, with reference to thermal energy transfer, why the pad is designed in this way.

Exam points

Explain conduction through particle vibrations and transfer of kinetic energy between neighbouring particles or atoms by interactions or collisions.
For metallic conduction, describe mobile electrons transferring energy through collisions with atoms or ions.
A shared carrier in good electrical and thermal conductors does not make charge flow and thermal-energy transport the same physical quantity.

[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.

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}

Exam points

Calculate wall heat loss using P = kAΔT/Δx, the temperature difference and a power unit such as W.
Calculate heat flux through ice using P/A = kΔT/Δx; convert cm to m and give W m⁻².
Explain why thicker ice lowers heat flux when conductivity and temperature difference stay fixed.
Use A ∝ d² to choose the curved P–diameter graph for rods of fixed length and end temperatures.

[Maximum number: 3]

A cylindrical cork of height H and cross-sectional area A is floating stationary in water. Its depth below the water surface is D.

(a)

On a winter day, the surface of a lake is frozen. The temperature of the air above the lake is $-6.0^{\circ} \mathrm{C}$ . The layer of ice frozen on the surface of the lake has a thickness of 1.9 cm .

[ 3 ]

(i)

The thermal conductivity of ice is $2.3 \mathrm{Wm}^{-1} \mathrm{~K}^{-1}$ . Calculate the rate per unit area at which thermal energy leaves the lake by conduction through the ice layer.

[ 2 ]

$\begin{aligned} \text { use of } \Delta \mathrm{T}=6<^{\circ} \mathrm{C} \gg \frac{\Delta Q}{\Delta t A}=\ll \frac{2.3 \cdot 6}{0.019}=\gg 730<\mathrm{W} \mathrm{~m}^{-2} \gg \end{aligned}$

(ii)

Explain how the rate per unit area at which thermal energy leaves the lake by conduction through the ice layer changes as the layer of ice grows thicker.

[ 1 ]

Exam points

In a stellar convection region, link the temperature gradient to hotter, less-dense plasma rising or cooler, denser plasma sinking.

[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

Use L = σAT⁴ with temperature in kelvin; doubling temperature multiplies emitted power by 16 at fixed area.
Distinguish total power σAT⁴ from power per unit area σT⁴; include area changes only for total power.
For spherical emitters use A = 4πR², convert radius to metres and retain the fourth power of temperature.
Compare stars using L₁/L₂ = (R₁/R₂)²(T₁/T₂)⁴; show both radius and temperature factors.
Rearrange stellar ratios carefully: R₁/R₂ = √(L₁/L₂)/(T₁/T₂)²; equal power at half the temperature needs four times the radius.
Use L and R ratios to find temperature with a fourth root; equal luminosity at lower temperature requires a larger emitting area.
Combine a Wien-law temperature with L = 4πR²σT⁴ when the preceding part supplies a spectral peak.
Convert emitted power to energy using E = LΔt; a one-second interval still requires the correct emitting area.
For net radiative loss to surroundings, use σA(T⁴ − Tsurroundings⁴), keeping both temperatures in kelvin.
Combine luminosity with inverse-square spreading: b = L/(4πd²) = σR²T⁴/d² for a spherical black-body star.
Balance mean absorbed flux with σT⁴; for a uniformly emitting sphere, intercepted disk area gives the factor of one quarter.
Match absorbing and emitting areas to the stated model; a normally illuminated surface patch differs from a whole isothermal sphere.
In a surface radiation balance, include atmospheric back radiation as well as absorbed sunlight before finding temperature.
With fixed albedo and emissivity, equilibrium temperature increases as the fourth root of incoming solar intensity.
On a log(L/R²) against log T graph, use the gradient to test the T⁴ law and the intercept to find 4πσ.
When comparing visible stellar and planetary brightness, distinguish emitted starlight from reflected sunlight; planets still emit thermal radiation.

[Maximum number: 4]

This question is in two parts. Part 1 is about solar radiation and the greenhouse effect. Part 2 is about a mass on a spring.

Part 1 Solar radiation and the greenhouse effect
The following data are available.

(a)

State the Stefan-Boltzmann law for a black body.

[ 2 ]

(b)

The average power absorbed per unit area at the Earth's surface is $240 \mathrm{Wm}^{-2}$ . By treating the Earth's surface as a black body, show that the average surface temperature of the Earth is approximately 250 K .

[ 2 ]

power radiated=power absorbed;
$T=\sqrt[4]{\frac{240}{5.7 \times 10^{-8}}}(=250 \mathrm{~K}) ;$

Marking guidance:

Accept answers given as 260 (K).

Exam points

To decide which star appears brighter, compare apparent brightness in W m⁻² and justify the choice with the greater received power per unit area.
For an unresolved binary, explain that light from both stars contributes to its apparent brightness; the system can outshine a comparison star.

[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 radiated in W, from apparent brightness, the received power per unit area in W m⁻².
Explain b = L/(4πd²) by spreading the emitted power over a sphere of radius d; keep source radius and observation distance distinct.
For a fixed source, scale brightness with inverse distance squared: one quarter of the distance gives sixteen times the brightness.
To keep brightness constant when luminosity changes, use d ∝ √L; halving source power requires distance d/√2.
Rearrange distance as d = √[L/(4πb)], convert units consistently and retain any luminosity multiplier read from the data or graph.
Use L = 4πd²b to infer emitted power, then divide by solar luminosity if solar units are requested.
For two sources, write b₁/b₂ = (L₁/L₂)(d₂/d₁)²; cancel distance only when the sources are approximately equidistant.
Justify which star appears brighter with a brightness ratio or two calculated values; luminosity alone does not decide the observation.
When graphs supply a source luminosity, read the required period and luminosity before applying the inverse-square distance calculation.
If luminosity is known, uncorrected absorption lowers measured brightness and makes the inverse-square distance estimate too large.
Apply reflection losses after finding solar flux at the orbital distance; distinguish a directly illuminated panel from a global mean.
Use the provided peak luminosity for peak apparent brightness and convert astronomical distances to metres before substitution.
Combine I ∝ amplitude² with inverse-square spreading when both source amplitude and observation distance change.

[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 $r=1.5 \times 10^{11} \mathrm{m}$ 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.

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

Exam points

Use λmaxT = 2.9×10⁻³ m K with temperature in kelvin and wavelength in metres; convert the final answer to the requested unit.
For a show-that temperature or wavelength, display the full substitution or enough significant figures to establish the stated approximation.
Determine stellar temperature by obtaining its spectrum, identifying the wavelength of maximum continuum intensity and applying Wien’s law.
Read λmax from the graph before calculating T; retain the wavelength-axis scale and the graph-reading tolerance.
Sketch a continuous, asymmetric black-body spectrum with one maximum, a steep short-wavelength side and a longer-wavelength tail.
For a hotter black body, move the peak to shorter wavelength and increase the emitted power; apply both conditions when choosing a graph.
When curves are normalised to the same maximum, preserve that height and use peak position to compare temperatures.
Use inverse ratios: doubling T halves λmax; raising T by about one third reduces λmax to about three quarters.
Combine Wien and Stefan–Boltzmann laws for the same body: halving peak wavelength doubles T and multiplies total emitted power by 16.
Use the emitting surface temperature and the supplied spectral peak; classify the resulting wavelength in the electromagnetic spectrum when asked.

[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.

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