IB Physics SL B.1.12 Conduction rate

Practise conduction calculations by using thermal conductivity, area, thickness and temperature difference to find energy transfer rates and read graph changes.

Exam points

use q/t = kAΔT/x to calculate conduction rate or rate per unit area, then give the final unit as W or W m^-2
use a temperature-distance graph gradient to infer conduction rate as ΔT falls during cooling
decide how changing thickness x in q/t = kAΔT/x alters the rate and the temperature gradient through a layer

[Maximum number: 3]

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.1.12—Conduction rate question 1 — IB Physics SL

(a)

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 .

[ 3 ]

(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)

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

[ 1 ]

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B.1.12—Conduction rate question 1

Question (a)

Question (i)

Question (ii)