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[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.

(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.

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 Topic Practice

Learn this topic

IB Physics SL B 1 Thermal Energy Transfers Topic Practice

Learn this topic

Question 1

Question (a)

Question (b)

Question (i)

Question (ii)

Question (iii)

Question (iv)

Question 2

Question 3