As the very first rudiment of climatology, estimate the temperature of Earth. Assume it is a perfect sphere and its temperature is uniform. Ignore the greenhouse effect. Thermal radiation from the Sun has an intensity (the "solar constant" S ) of about 1370 W/m 2 at the radius of Earth's orbit. (a) Assuming the Sun's rays are parallel, what area must S be multiplied by to get the total radiation intercepted by Earth? It will be easiest to answer in tens of Earth's radius, R . (b) Assume that Earth reflects about 30% of the solar energy it intercepts. In other words, Earth has an albedo with a value of A = 0.3 . In terms of S , and R , what is the rate at which Earth absorbs energy from the Sun? (c) Find the temperature at which Earth radiates energy at the same rate. Assume that at the infrared wavelengths where it radiates, the emissivity e is 1. Does your result show that the greenhouse effect is important? (d) How does your answer depend on the area of Earth?
As the very first rudiment of climatology, estimate the temperature of Earth. Assume it is a perfect sphere and its temperature is uniform. Ignore the greenhouse effect. Thermal radiation from the Sun has an intensity (the "solar constant" S ) of about 1370 W/m 2 at the radius of Earth's orbit. (a) Assuming the Sun's rays are parallel, what area must S be multiplied by to get the total radiation intercepted by Earth? It will be easiest to answer in tens of Earth's radius, R . (b) Assume that Earth reflects about 30% of the solar energy it intercepts. In other words, Earth has an albedo with a value of A = 0.3 . In terms of S , and R , what is the rate at which Earth absorbs energy from the Sun? (c) Find the temperature at which Earth radiates energy at the same rate. Assume that at the infrared wavelengths where it radiates, the emissivity e is 1. Does your result show that the greenhouse effect is important? (d) How does your answer depend on the area of Earth?
As the very first rudiment of climatology, estimate the temperature of Earth. Assume it is a perfect sphere and its temperature is uniform. Ignore the greenhouse effect. Thermal radiation from the Sun has an intensity (the "solar constant" S) of about 1370 W/m2 at the radius of Earth's orbit. (a) Assuming the Sun's rays are parallel, what area must S be multiplied by to get the total radiation intercepted by Earth? It will be easiest to answer in tens of Earth's radius, R. (b) Assume that Earth reflects about 30% of the solar energy it intercepts. In other words, Earth has an albedo with a value of
A
=
0.3
. In terms of S, and R, what is the rate at which Earth absorbs energy from the Sun? (c) Find the temperature at which Earth radiates energy at the same rate. Assume that at the infrared wavelengths where it radiates, the emissivity e is 1. Does your result show that the greenhouse effect is important? (d) How does your answer depend on the area of Earth?
Assume, the average radiation intake of the planet earth increases by 120 W/m² momentarily. The planet therefore leaves its thermal equilibrium and starts heating up
(neglect additional thermal losses).
The total weight of the planet is 6 x 1024 kg. Assume, that we have 1.1 x 109 km³ of sea water and the rest of the planet is rock. The heat capacity of sea water is 3.6 kJ/
kg K, the density is 1 t/m³. The heat capacity of rock is 1.1 kJ/ kg K, the density is 2.9 t/m².
Take the cross section area of the planet as A = r² with r being 6500 km.
How long does it take, until the temperature of the earth has risen by 3°C? Assume, the full mass of the planet is always on the same temperature. Why is the result much
lower than you'd expect? Which of the assumptions is not realistic?
The radiation energy (intensity of the radiation) reaching Earth from the sun at the top of the atmosphere is 1.36×103??2⁄, which is called the solar constant. Assuming that Earth absorbs the total power coming from the Sun to the Earth and radiates with the emissivity of 0.8 at a uniform temperature around the Earth, what would the equilibrium temperature of Earth be?
Use the value of the solar energy flux on Earth to determine the radius of the Sun.
Assuming that the Sun's temperature is 5780 K and that its emissivity is 1, find its radius in kilometers. Neglect the temperature of the environment.
Physics for Scientists and Engineers: A Strategic Approach, Vol. 1 (Chs 1-21) (4th Edition)
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