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.
Answers
Given: Luminosity is 3.828 x 10^26 Watt, radius of sun is 696 x 10^3 km and radius of earth is 6370 km.
To find: Amount of energy arriving on the Earth in a single day, to how many litres of heating oil is this equivalent, the Earth reflects 30% of this energy: Determine the temperature on Earth’s surface and what other factors should be considered to get an even more precise temperature estimate ?
Solution:
- Now we know the formula for solar constant, that is:
Solar Constant = E(0) = L / 4πr²
So putting the values in it, we get:
Solar Constant = 3.828 x 10^26 / 4 π( 1.495 x 10^11) ²
Solar Constant = 1.36 x 10 W/m³
- Now multiplying the amount by the area of Earth cross-section -
E0 = πR² x 86400s = 1.5 x 10^22 J
- Now the heating oil is this equivalent to:
N = E / 37.3 x 10^6
N = 4 x 10^14
- Now formula for energy absorbed by earth is:
πR² x ( 1 - A) = 1.2 × 10^17
- Therefore,
E0. πR² x ( 1 - A) = 4πR²T^4
T = √E0 ( 1 - A) /4 = 254 k
T = -18° C
- The average Earth temperature is around 15°. We should consider the human energy production, the geothermal heat, and the earth's internal heat.
Answer:
So amount of energy arriving on the Earth in a single day is 1.5 x 10^22 J, 4 x 10^14 litres of heating oil is this equivalent, the temperature on Earth’s surface is -18° C.