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Study B.1 Thermal energy transfers conceptsOpen the corresponding Concept lesson for explanations, examples and exam connections.

[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 ]

$4.9 \times 10^{-21}<\mathrm{J} \%$

[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]

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

-373 K

-173 K

173 K

$373 \mathrm{~K}$

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IB Physics HL B 1 Thermal Energy Transfers Topic Practice

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