IBDP Physics 8.2 – Thermal energy transfer: IB style Question Bank HL Paper 2

a.

power/energy per second emitted is proportional to surface area;
and proportional to fourth power of absolute temperature / temperature in K;
Accept equation with symbols defined.

solar power given by \(4\pi {R^2}\sigma {T^4}\);
spreads out over sphere of surface area \(4\pi {d^2}\);
Hence equation given.

\(\left( {\frac{{\sigma {R^2}{T^4}}}{{{d^2}}} = } \right)\frac{{5.7 \times {{10}^{ – 8}} \times {{\left[ {7.0 \times {{10}^8}} \right]}^2} \times {{\left[ {5.8 \times {{10}^3}} \right]}^4}}}{{{{\left[ {1.5 \times {{10}^{11}}} \right]}^2}}}\);

=1.4×10³(Wm^-2);

Award [2] for a bald correct answer.

some energy reflected;
some energy absorbed/scattered by atmosphere;
depends on latitude;
depends on time of day;
depends on time of year;
depends on weather (eg cloud cover) at location;
power output of Sun varies;
Earth-Sun distance varies;

power radiated=power absorbed;
\(T = {}^4\sqrt {\frac{{240}}{{5.7 \times {{10}^{ – 8}}}}} \left( { = 250{\rm{K}}} \right)\);

Accept answers given as 260 (K).

radiation from Sun is re-emitted from Earth at longer wavelengths;
greenhouse gases in the atmosphere absorb some of this energy;
and radiate some of it back to the surface of the Earth;

(i) gravitational force / gravitational attraction / weight; (do not accept gravity)

(ii) astronauts and spaceship have the same acceleration;
acceleration is towards (centre of) planet;
so no reaction force between astronauts and spaceship;

or

astronauts and spaceships are both falling towards the (centre of the) planet;
at the same rate;
so no reaction force between astronauts and spaceship;

gravitational force equated with centripetal force / \(\frac{{GmM}}{{{r^2}}} = \frac{{m{v^2}}}{r}\);

\( \Rightarrow {v^2} = \frac{{GM}}{r} \Rightarrow \left( {v = \sqrt {\frac{{GM}}{r}} } \right)\);

(i) thermal energy is lost;
total energy decreases;

(ii) since E decreases, r also decreases;
as r decreases v increases / E_k increases so v increases;