IB Physics SL B 1 Thermal Energy Transfers Questions

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.

Exam points

Use molecular models to explain states, density and internal energy.
Convert Celsius and kelvin temperatures; link kelvin temperature to mean particle kinetic energy.
Identify thermal-transfer direction and explain energy changes during phase changes.
Use Q=mcΔT and Q=mL for heating, cooling and phase changes, including staged energy calculations.
Explain conduction, convection and radiation; calculate conduction rate from conductivity, area, thickness and ΔT.
Use black-body power and b=L/(4πd²) to relate luminosity, apparent brightness and distance.
Apply Wien’s law, λmaxT=2.9×10−3 m K, to infer temperature or peak wavelength.

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

[Maximum number: 10]

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)

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 $10^{\circ} \mathrm{C}$ .

[ 2 ]

(b)

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 .

[ 8 ]

(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)

The depth of water below the ice is 22 m and its average initial temperature is $2.0^{\circ} \mathrm{C}$ . Estimate the minimum thermal energy per unit area that must be removed to freeze all the water in the lake.

The following data are available:

\begin{aligned} \text { Specific heat capacity of water } & =4.2 \times 10^{3} \mathrm{Jkg}^{-1} \mathrm{~K}^{-1} \\ \text { Latent heat of fusion of water } & =3.3 \times 10^{5} \mathrm{Jkg}^{-1} \\ \rho_{\text {water }} & =1000 \mathrm{~kg} \mathrm{~m}^{-3} \end{aligned}

Layers of ice on lakes do not grow thicker than a small percentage of the lake's depth even when the exterior temperature remains constant below the freezing point for some time.

[ 3 ]

$\begin{aligned} \mathrm{m}=(\rho \mathrm{A})(22)=(1000)(\mathrm{A})(22)=22000 \mathrm{~A} \text { AND } \Delta \mathrm{T}=2<^{\circ} \mathrm{C} \gg \mathrm{Q} / \mathrm{A}=<\mathrm{mc} \Delta \mathrm{~T}>=(22)(1000)\left(4200^{*} 2\right)=1.85 \times 10^{8}<\mathrm{J} \mathrm{~m}^{-2}> \text { OR } \mathrm{Q} / \mathrm{A}=<\mathrm{mL}>=(22)(1000)(330000)=7.26 \times 10^{9} \ll \mathrm{~J} \mathrm{~m}^{-2}> \mathrm{Q} / \mathrm{A}=7.4 \times 10^{9}<\mathrm{J} \mathrm{~m}^{-2}> \end{aligned}$

(iii)

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 ]

(iv)

Discuss why the anomaly in the value of the density of water supports life in water on Earth.

[ 2 ]

if solid water were denser than liquid, ice layer would sink OR

water at $4^{\circ} \mathrm{C}$ sinks to bottom

ice layer «would isolate water below ice to» maintain conditions «above freezing »

this insulates the lake OR prevents the lake from freezing completely

[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}

[Maximum number: 1]

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

-373 K

-173 K

173 K

$373 \mathrm{~K}$

[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.

[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

[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}}

[Maximum number: 2]

Distinguish between internal energy and thermal energy (heat).

Internal energy:
Thermal energy:

[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;

[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.

[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}}

[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.

[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}

[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.

[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).

[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.

[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 $\nS=1.4 \times 10^{3} \mathrm{Wm}^{-2}\n$

[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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Covered syllabus points

Question 1

Question (a)

Question (b)

Question (i)

Question (ii)

Question (iii)

Question (iv)

Question 2

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Question 12

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Question 14

Question (a)

Question (b)

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Question 17