IB Physics HL B.1 Thermal Energy Transfers

[Maximum number: 9]

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}

(a)

Determine the mean temperature of Ceres assuming that it acts as a black-body radiator.

[ 3 ]

average intensity at Ceres orbit $=\left(\frac{3.8 \times 10^{26}}{4 \times \pi \times\left(4.4 \times 10^{11}\right)^{2}}\right) \lessdot=156 \mathrm{Wm}^{-2} \| \vee$ average incident intensity $=\frac{156}{4}=\ll 39 \gg$

temperature $<=\left(\frac{39}{5.67 \times 10^{-8}}\right)^{\frac{1}{4}}>=160 \ll \mathrm{~K} \gg$

Marking guidance:

Allow ECF from MP1 and MP2

(b)

Ceres has a solid rocky core covered with solid ice. The mean temperature is higher than your answer in (a)(i) because radioactive nuclei in the centre of Ceres are decaying. Outline how the energy from the radioactive decay reaches the surface.

[ 2 ]

(c)

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

[ 4 ]

(i)

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

[ 3 ]

(ii)

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.

[ 1 ]

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

[Maximum number: 3]

(a)

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.

[ 1 ]

(i)

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

[ 1 ]

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

(b)

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 $4.5 \times 10^{9} \mathrm{~J}$ .

[ 2 ]

(i)

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 $500 \mathrm{Jkg}^{-1} \mathrm{~K}^{-1}$ .

[ 2 ]

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

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

[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?

A

699 K

B

426 K

C

153 K

D

120 K

[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.

[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

[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}

[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:

[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.

[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.

[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

[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 ]

[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.

[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

[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: 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.

[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 $r=1.5 \times 10^{11} m$ 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
$S=1.4 \times 10^{3} \mathrm{Wm}^{-2}$

[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.

IB Physics HL B 1 Thermal Energy Transfers Questions

Exam points

Covered syllabus points

Covered syllabus points

Question 1

Question (a)

Question (b)

Question (c)

Question (i)

Question (ii)

Question 2

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Question (i)

Question (b)

Question (i)

Question 3

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Question 5

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Question 9

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Question 11

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Question 12

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Question 18