IB Physics HL B the Particulate Nature of Matter Questions

Practise IB Physics HL particle models through shared-core and HL work on gases, thermal energy, circuits, radiation and power, using data precisely.

Exam points

Use particle models to connect molecular motion, spacing and collisions with temperature, internal energy, gas pressure and electrical charge transport.
Analyse heat and work in closed systems and cycles using the first and second laws, p–V diagrams, entropy and energy-conservation data.
Calculate thermal and radiative energy transfers with phase-change, conduction, convection, black-body, greenhouse and Stefan–Boltzmann evidence.
Solve multi-state and microscopic gas problems with pV/T, PV=nRT or PV=NkBT, and evaluate ideal-gas assumptions from pressure, density and temperature.
Build and test extended circuit models using Kirchhoff rules, component and source equations, V–I graphs, resistivity, power, energy and rms quantities.

Covered syllabus points

B.1 Thermal energy transfers B.2 Greenhouse effect B.3 Gas laws B.4 Thermodynamics B.5 Current and circuits

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Study B. The particulate nature of matter 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: 1]

The diagram shows a simple model of the energy balance in the Earth surface-atmosphere system. The intensities of the radiations are given.

What is the average intensity radiated by the atmosphere towards the surface?

$100 \mathrm{Wm}^{-2}$

$150 \mathrm{Wm}^{-2}$

$240 \mathrm{Wm}^{-2}$

$390 \mathrm{Wm}^{-2}$

[Maximum number: 7]

A boat is moved from land to water by rolling it across a set of cylindrical airbags.

(a)

When fully inflated, an unloaded airbag has a diameter of 1.80 m and a length of 24.0 m . At a temperature of $15^{\circ} \mathrm{C}$ , an airbag can hold 4200 mol of gas.

[ 7 ]

(i)

Show that the pressure in an airbag is about 0.2 MPa .

When the boat is placed on the airbags, the airbags are compressed so that the effective contact area is as shown in the diagram.

In this arrangement, the maximum safe pressure before an airbag bursts is four times the value calculated in (a)(i). The boat is supported by airbags on a slope that is at an angle of $4.0^{\circ}$ to the horizontal. There are fifteen airbags supporting the boat at all times.

[ 2 ]

$\begin{aligned} V=\pi r^{2} h=\pi 0.9^{2} \times 24=61.07 \mathrm{~m}^{3} P=\frac{(4200)(8.31)(273+15)}{61.07}=0.16 \mathrm{MPa} \end{aligned}$

Allow MP1 to be seen in MP2.

(ii)

Estimate the maximum safe mass that this arrangement can hold.

[ 3 ]

$\begin{aligned} \mathrm{F}=4 P A=4\left(1.6 \times 10^{5}\right)(15 \times 24 \times 1.8)=4.14 \times 10^{8} \mathrm{~N} \mathrm{F}=m g \cos \theta=\mathrm{m}(9.8)(\cos 4)=9.78 \mathrm{~m} \mathrm{~N} m=\frac{4 P A}{g \cos \theta}=\frac{4.14 \times 10^{8}}{9.78}=4.3 \times 10^{7} \mathrm{~kg} \end{aligned}$

Do not award MP2 if the cos θterm is omitted.

Allow ECF for MP3.

(iii)

Outline the change in internal energy of the gas in the airbag.

[ 2 ]

Internal energy / U decreases

$\Delta \mathrm{Q}=0$ and therefore $\Delta \mathrm{U}=-\mathrm{W}$

OR

«Adiabatic expansion causes» T decreases

[Maximum number: 16]

This question is in two parts

(a)

The plates in (c) are replaced by a cell that has an emf of 12.0 V and internal resistance $5.00 \Omega$ . A resistor of resistance R is connected in series with the cell. The energy transferred by the cell to an electron as it moves through the resistor is $1.44 \times 10^{-18} \mathrm{~J}$ .

[ 6 ]

(i)

Define resistance of a resistor.

[ 1 ]

ratio potential difference/voltage (across resistor) to current (in resistor) / $\frac{V}{I}$
with symbols defined;

(ii)

Show that the value of R is $15.0 \Omega$ .

[ 4 ]

pd across $R=\frac{1.44 \times 10^{-18}}{1.6 \times 10^{-19}}=9.00 \mathrm{~V}$ ;
pd across internal resistance $=12.0-9.00=3.00 \mathrm{~V}$ ;
current in circuit $=\frac{3.00}{5.00}=0.600 \mathrm{~A}$ ;
$R=\frac{9.00}{0.600}=15.0 \Omega$ ;

(iii)

Calculate the total power supplied by the cell.

[ 1 ]

(b)

A gas undergoes a thermodynamic cycle. The P-V diagram for the cycle is shown below.

In the changes of state B to C and D to A , the gas behaves as an ideal gas and the changes in state are adiabatic.

[ 3 ]

(i)

State the circumstances in which the behaviour of a gas approximates to ideal gas behaviour.

[ 2 ]

(ii)

State what is meant by an adiabatic change of state.

[ 1 ]

(c)

With reference to the first law of thermodynamics, explain for the change of state A to B, why energy is transferred from the surroundings to the gas.

[ 4 ]

(d)

Estimate the total work done in the cycle.

[ 3 ]

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