IB Physics SL B.1 Thermal Energy Transfers Question Bank

[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.

Figure for Question B.1 Thermal energy transfers 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 .

[ 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 calculated in (e)(i) 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

2 max

[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.1 Thermal energy transfers question 2 — 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: 1]

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

-373 K

-173 K

173 K

$373 \mathrm{~K}$

IB Physics SL B.1 Thermal Energy Transfers Question Bank

Exam points

Covered syllabus points

Covered syllabus points

B.1 Thermal energy transfers question 1

Question (a)

Question (b)

Question (i)

Question (ii)

Question (iii)

Question (iv)

B.1 Thermal energy transfers question 2

B.1 Thermal energy transfers question 3