IB Physics SL B: Particulate Nature of Matter

[Maximum number: 8]

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

Figure for Question B. The particulate nature of matter question 1 — IB Physics SL

(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 .

[ 6 ]

(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 calculated in (e)(i) changes as the layer of ice grows thicker.

[ 1 ]

[Maximum number: 1]

In an energy-balance climate model, the power of the incoming radiation over an area A is $P_{\mathrm{i}}$ and the power of the outgoing radiation over the same area is $P_{\mathrm{o}}$ . The surface heat capacity is $C_{\mathrm{s}}$ . What is the time taken to increase the temperature of the area by $\theta$ ?

A

$\frac{\left(P_{\mathrm{i}}-P_{\mathrm{o}}\right)}{C_{\mathrm{s}} \theta}$

B

$\frac{C_{\mathrm{s}} \theta}{\left(P_{\mathrm{i}}-P_{\mathrm{o}}\right)}$

C

$\frac{A C_{\mathrm{s}} \theta}{\left(P_{\mathrm{i}}-P_{\mathrm{o}}\right)}$

D

$\frac{A\left(P_{\mathrm{i}}-P_{\mathrm{o}}\right)}{C_{\mathrm{s}} \theta}$

[Maximum number: 9]

A solid cylinder of height h and density $\rho$ rests on a flat surface.

Figure for Question B. The particulate nature of matter question 3 — IB Physics SL

(a)

Show that the pressure $p_{\mathrm{C}}$ exerted by the cylinder on the surface is given by $p_{\mathrm{C}}=\rho g h$ .

[ 2 ]

weight of cylinder $=A h g \rho$ $\text { pressure }=\frac{F}{A}=\frac{A h g \rho}{A}$

Marking guidance:

Allow use of $A=\pi r^{2}$ in MP1.

(b)

A tube of constant circular cross-section, sealed at one end, contains an ideal gas trapped by a cylinder of mercury of length 0.035 m . The whole arrangement is in the Earth's atmosphere. The density of mercury is $1.36 \times 10^{4} \mathrm{~kg} \mathrm{~m}^{-3}$ .

When the mercury is above the gas column the length of the gas column is 0.190 m .

[ 7 ]

(i)

Show that $\left(p_{\mathrm{o}}+p_{\mathrm{m}}\right) \times 0.190=\frac{n R T}{A}$ where
$p_{\mathrm{o}}=$ atmospheric pressure
$p_{\mathrm{m}}=$ pressure due to the mercury column
T= temperature of the trapped gas
n= number of moles of the trapped gas
A= cross-sectional area of the tube.

[ 2 ]

use of PV=nRT and V= Area × (0.190) seen substitution of $\mathrm{P}=p_{\mathrm{o}}+p_{\mathrm{m}}$ «re-arrangement to give answer»

(ii)

The tube is slowly rotated until the gas column is above the mercury.

Figure for Question (ii) — IB Physics SL

The length of the gas column is now 0.208 m . The temperature of the trapped gas does not change during the process.

Determine the atmospheric pressure. Give a suitable unit for your answer.

[ 4 ]

recognition that $\frac{\mathrm{nRT}}{\mathrm{A}}$ is constant $\boldsymbol{OR} 190 p_{\mathrm{o}}+190 p_{\mathrm{m}}=208 p_{0}-208 p_{\mathrm{m}}$ OR $p_{0}=\frac{398}{18} p_{\mathrm{m}}$

pressure due to mercury $p_{\mathrm{m}}=0.035 \times 1.36 \times 10^{4} \times 9.81\left(=4.67 \times 10^{3} \mathrm{~Pa}\right) 1.03 \times 10^{5}$ $\mathrm{Pa} \boldsymbol{O} \boldsymbol{R} \mathrm{Nm}^{-2} \boldsymbol{O} \boldsymbol{R} \mathrm{kgm}^{-1} \mathrm{~s}^{-2} \boldsymbol{}$

Marking guidance:

Do not award for a bald correct answer. Working must be shown to award MP3.

Award MP4 for any correct unit of pressure (eg "mm of mercury / Hg").

(iii)

Outline why the gas particles in the tube hit the mercury surface less often after the tube has been rotated.

[ 1 ]

[Maximum number: 8]

This question is in two parts. Part 1 is about a thermistor circuit. Part 2 is about vibrations and waves.
Part 1 Thermistor circuit
The circuit shows a negative temperature coefficient (NTC) thermistor X and a $100 \mathrm{k} \Omega$ fixed resistor R connected across a battery.

Figure for Question B. The particulate nature of matter question 4 — IB Physics SL

The battery has an electromotive force (emf) of 12.0 V and negligible internal resistance.

(a)

Define electromotive force (emf).

[ 1 ]

(b)

The graph below shows the variation with temperature T of the resistance $R_{\mathrm{x}}$ of the thermistor.

[ 7 ]

(i)

Determine the temperature of X when the potential difference across R is 4.5 V .

[ 4 ]

$V_X = 7.5\ ext{V}$ .
$I = \frac{4.5}{100 imes 10^3} = 4.5 imes 10^{-5}\ ext{A}$ OR $\frac{V_X}{V_R}=\frac{R_X}{R_R}$ .
$R_X = \frac{7.5}{4.5 imes 10^{-5}} = 1.67 imes 10^5\ \Omega$ OR $R_X=\frac{7.5}{4.5} imes100 imes10^3=1.67 imes10^5\ \Omega$ .
T=-37 or $-38\ ^\circ ext{C}$ .

(ii)

State the range of temperatures for which the change in the resistance of the thermistor is most sensitive to changes in temperature.

[ 1 ]

50 to (up to) $-30^{\circ} \mathrm{C} /$ at low temperatures;

(iii)

State and explain the effect of a decrease in temperature on the ratio

\frac{\text { voltage across } \mathrm{X}}{\text { voltage across } \mathrm{R}}

Part 2 Vibrations and waves

The cone and dust cap D of a loudspeaker L vibrates with a frequency of 1.25 kHz with simple harmonic motion (SHM).

Figure for Question (iii) — IB Physics SL

[ 2 ]

as the temperature decreases $R_{X}$ increases; same current through R and X so the ratio increases or $V_{X}$ increases and $V_{R}$ decreases so the ratio increases;

Part 2 Vibrations and waves

[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.

Table for Question B. The particulate nature of matter question 5 — IB Physics SL

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: 10]

The diagram shows a simplified energy-balance model for the Earth surface–atmosphere system.

Figure for Question B. The particulate nature of matter question 6 — IB Physics SL

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}

(a)

State what is meant by the solar constant.

[ 1 ]

(b)

Outline the physical mechanism by which some of the radiation emitted by the surface is absorbed by greenhouse gases in the atmosphere and re-radiated towards the surface.

[ 2 ]

(c)

Show that the average global intensity of radiation absorbed by the surface is about $240 \mathrm{Wm}^{-2}$ .

[ 2 ]

Average incoming intensity $=\frac{S}{4}$ « $=340 \mathrm{~W} \mathrm{~m}^{-2}$ »

Absorbed intensity $=(1-0.30) \times 340$ or $238 \mathrm{~W} \mathrm{~m}^{-2}$

The steps in the calculation must be
shown.

(d)

Determine the average intensity re-radiated by the atmosphere towards the surface. Assume that the emissivity of the surface is 0.90 .

[ 3 ]

Emitted intensity $=\ll 5.67 \times 10^{-8} \times 0.90 \times 288^{4}=>351 \mathrm{~W} \mathrm{~m}^{-2}$

Intensity leaving Earth $=238 \mathrm{~W} \mathrm{~m}^{-2}$

Re-radiated intensity $=\ll 351-238=>113 \mathrm{~W} \mathrm{~m}^{-2}$

Marking guidance:

Ignore units as they are not required for
the answer.
The steps in the calculation must be
checked.
Accept outgoing intensity $=240 \mathrm{~W}$ $m^{-2}$ for MP2.

(e)

Show, with reference to the solar constant, that the total power radiated by the Sun is about $4 \times 10^{26} \mathrm{~W}$ .

[ 2 ]

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

IB Physics SL B: The Particulate Nature of Matter

Covered syllabus points

Covered syllabus points

B. The particulate nature of matter question 1

Question (a)

Question (b)

Question (i)

Question (ii)

Question (iii)

B. The particulate nature of matter question 2

B. The particulate nature of matter question 3

Question (a)

Question (b)

Question (i)

Question (ii)

Question (iii)

B. The particulate nature of matter question 4

Question (a)

Question (b)

Question (i)

Question (ii)

Question (iii)

B. The particulate nature of matter question 5

B. The particulate nature of matter question 6

Question (a)

Question (b)

Question (c)

Question (d)

Question (e)