DP Physics (last assessment 2024)

Question 21M.2.SL.TZ1.4

Date	May 2021	Marks available	[Maximum mark: 6]	Reference code	21M.2.SL.TZ1.4
Level	SL	Paper	2	Time zone	TZ1
Command term	Calculate, Derive, Explain	Question number	4	Adapted from	N/A

[Maximum mark: 6]

21M.2.SL.TZ1.4

A planet orbits at a distance d from a star. The power emitted by the star is P. The total surface area of the planet is A.

(a.i)

Explain why the power incident on the planet is

$\frac{P}{4 π d^{2}} \times \frac{A}{4} .$

[2]

Markscheme

$\frac{P}{4 π d^{2}}$ is the power received by the planet/at a distance d «from star» ✓

$\frac{A}{4}$ is the projected area/cross sectional area of the planet ✓

(a.ii)

The albedo of the planet is $α_{p}$ . The equilibrium surface temperature of the planet is T. Derive the expression

$T = \sqrt[4]{\frac{P (1 - α_{p})}{16 π d^{2} e σ}}$

where e is the emissivity of the planet.

[2]

Markscheme

use of $e σ A T^{4} OR \frac{P}{4 π d^{2}} \times \frac{A}{4} \times (1 - α_{p})$ ✓

with correct manipulation to show the result ✓

(b)

On average, the Moon is the same distance from the Sun as the Earth. The Moon can be assumed to have an emissivity e = 1 and an albedo $α_{M}$ = 0.13. The solar constant is 1.36 × 103 W m⁻². Calculate the surface temperature of the Moon.

[2]

Markscheme

$\sqrt[4]{\frac{1.36 \times 10^{3} \times 0.87}{4 \times 5.67 \times 10^{- 8}}}$ ✓

T = 268.75 «K» ≅ 270 «K» ✓

Syllabus sections

Core

Core » Topic 8: Energy production » 8.2 – Thermal energy transfer

Core » Topic 8: Energy production

Question 21M.2.SL.TZ1.4

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