Question

Our Sun shines bright with a luminosity of 3.828 x 1026 Watt. Her energy is responsible for many processes and the habitable temperatures on the Earth that make our life possible. (a) Calculate the amount of energy arriving on the Earth in a single day. (b) To how many litres of heating oil (energy density: 37.3 x 106 J/litre) is this equivalent? (c) The Earth reflects 30% of this energy: Determine the temperature on Earth’s surface. (d) What other factors should be considered to get an even more precise temperature estimate? Note: The Earth’s radius is 6370 km; the Sun’s radius is 696 x 103 km; 1 AU is 1.495 x 108 km.

Answer 1

We have;

Luminosity of the Sun = L = $3.828$ x $10^2^6$ W

Radius of the Sun = 696 x 103 km

Radius of the Earth = 6370 km

(We will solve the problem serially)

(a) Amount of energy arriving on the Earth in one day

We know,

Solar Constant = E0 = $\frac{L}{4}$$\pi r^2$ = $\frac{3.828 * 10`26}{4}$ $\pi$ (1.495 . 10`11)² = 1.36 × 10 $W/m^3$

On multiplying it with the area of Earth cross-section, we get;

E0 = $\pi R^2$ × 86400 s  = $1.5$ × $10^2^2$ J

(b) Equivalence of heating oil with the energy

Then,

N =  $\frac{E }{37.3 * 10^6}$ = $4$ × $10^1^4$

(c) Temperature of Earth's surface

Amount of energy absorbed by the earth = $\pi R^2$. (1 - A) = $1.2$ × $10^1^7$

∴ E0.  $\pi R^2$. (1 - A) = $4\pi R^2T^4$

⇒ T = $\sqrt{E0}$ (1 - A) ÷ 4 = 254 k = - 18° C

(d) As we know, the average Earth temperature is approximately 15° C. Due to the greenhouse effect, there is inconsistency between these two figures. Some other factors to be considered are the production of energy by artificial methods, energy produced by living organisms themselves (plants, animals, humans, and other life forms), the geothermal energy, as well as the heat within the earth itself.

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