1. (a) What is the rate at which the Sun delivers energy to the entire Earth...

1. (a) What is the rate at which the Sun delivers energy to the entire Earth ? Assume that all of the incident energy is absorbed. (b) From the internet (or whatever information source handy), find out the total rate at which energy is used by humans per second, and compare with your estimate in Part (a). What area of solar panels would be required to provide all the power required by the Earth’s population ? (Assume the panels have an effeciency of 100 %).

Solutions

Expert Solution

a) The energy radiated by the sun is given by the Stephan Boltzmann equation

R_s = Radius of Sun = 6.96 *10⁸ m

Stephan Boltzmann's constant =5.67*10^-8 Wm^-2 K^-4

T surface temperature of sun = 5,778 K

Therefore L_s = 3.857 *10²⁶ W

At the Earth the Solar power than reaches us

where d is distance between sun and earth = 1.5*10¹¹ m , R_E Radius of earth = 6.37 *10⁶ m

= 1.735*10¹⁷ J/s Answer

b) The world consumed 5.67 × 10²⁰ J in 2013. Therefore 5.67 × 10²⁰ / (365*86400) J/s = 1.8 × 10¹³ J

Therefore 1.04 x 10^-4 fraction of the energy incident is used.

At a time half of the earth is irradiated. Therefore the energy per m² of area at the equator is given by

The Area of solar panels need to be near the equator and Area reuired is

Or 2.646 *10⁴ km² (As both halves of the earth need to be covered) Answer

genius_generous answered 1 year ago

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