Question

What is the energy contained in a 1.30 m3 volume near the Earth's surface due to radiant energy from the Sun

Answer 1

The energy contained is 5.856 x 10⁻⁶ J

Step-by-step explanation:

Average energy density of electromagnetic radiation per unit volume is given by the equation;

`U_(avg) = (1)/(2) \epsilon _o E_o`²

where;

`\epsilon _o` is permittivity of free space

`E_o` is maximum electric field strength, this can be calculated from the intensity of sun reaching the Earth's surface.

`E_o = \sqrt{(2I)/(\epsilon_o C) }`

The intensity of sun reaching the Earth is 1350 W/m²

`E_o = \sqrt{(2*1350)/(8.885*10^(-12)*3*10^8 ) } \\\\E_o = 1008.96 \ V/m\\`

Average energy density of electromagnetic radiation per unit volume;

`U_(avg) = (1)/(2) \epsilon_o E_o^2\\\\U_(avg) = (1)/(2) (8.85*10^(-12))(1008.96)^2\\\\U_(avg) = 4.505 *10^(-6) \ J/m^3`

The energy contained in a 1.30 m³ volume is given by;

E = (4.505 x 10⁻⁶)(1.3)

E = 5.856 x 10⁻⁶ J

Therefore, the energy contained is 5.856 x 10⁻⁶ J