The intensity of the Sun’s radiation at the position of the Earth is approximately 1400 W m⁻².

Suggest why the average power received per unit area of the Earth is 350 W m⁻².

The diagram shows a simplified model of the energy balance of the Earth’s surface. The diagram shows radiation entering or leaving the Earth’s surface only.

The average equilibrium temperature of the Earth’s surface is T_E and that of the atmosphere is T_A = 242K.

(i) Using the data from the diagram, state the emissivity of the atmosphere.

(ii) Show that the intensity of the radiation radiated by the atmosphere towards the Earth’s surface is 136Wm⁻².

(iii) By reference to the energy balance of the Earth’s surface, calculate T_E.

(i) Outline a mechanism by which part of the radiation radiated by the Earth’s surface is absorbed by greenhouse gases in the atmosphere.

(ii) Suggest why the incoming solar radiation is not affected by the mechanism you outlined in (c)(i).

(iii) Carbon dioxide (CO₂) is a greenhouse gas. State one source and one sink (object that removes CO₂) of this gas.

the solar radiation is captured by a disc of area πR² where R is the radius of the Earth;
but is distributed (when averaged) over the entire Earth’s surface which has an area four times as large;
Award [1] for reference to absorption/reflection.

(i) 0.700;

(ii) I(= eσT_a⁴)=0.70×5.67×10⁻⁸×242⁴;
=136Wm⁻²

(iii) σT_e ⁴=136+245Wm⁻²;
hence \({T_e}\left( { = \sqrt[4]{{\frac{{381}}{{5.67 \times {{10}^{ - 8}}}}}}} \right) = 286{\rm{K}}\);

(i) the Earth radiates radiation in the infrared region of the spectrum; the greenhouse gases have energy level differences (in their molecular energy levels) corresponding to infrared energies;
and so the infrared photons are absorbed;
or
the Earth radiates photons of infrared frequency;
the greenhouse gas molecules oscillate/vibrate with frequencies in the infrared region;
and so because of resonance the photons are absorbed;

(ii) most incoming radiation consists of photons in the visible/ultraviolet region /photons of much shorter wavelength than those radiated by the Earth / photons of different wavelength of that radiated by Earth;
and so these cannot be absorbed;

(iii) Source: emissions from volcanoes/burning of fossil fuels in power plants/cars/breathing;
Sink: oceans / rivers / lakes / seas / trees;