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
Answer:
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(a) Amount of energy arriving on the Earth in a single day = 1.5 * 10^22 J
(b) To how many liters of heating oil is this equivalent = 4 * 10^14 liters
(c) Temperature on Earth’s surface = - 18° C
(d) Other factors to consider to get a precise temperature estimate - human energy production, geothermal heat and the Earth's internal heat
Explanation:
Given:
Luminosity = 3.828 * 10^26 Watt.
Radius of Sun = 696 * 10^3 km
Radius of Earth = 6370 km
1 AU is 1.495 *10^8 km.
Find:
(a) Amount of energy arriving on the Earth in a single day.
(b) To how many liters of heating oil 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
Solution:
a) Solar Constant = Eo = L/4πr²
= 3.828 * 10^26/ 4 π (1.495 * 10^11) ²
= 1.36 * 10 W/m³
Multiplying the amount by the area of Earth cross-section:
Eo = πR² * 86400s = 1.5 * 10^22 J
b) N = E/ 37.3 * 10^6
= 4 * 10^14
c) Energy absorbed by earth = πR². ( 1 - A) = 1.2 * 10^17
So Eo. πR². ( 1 - A) = 4πR²T^4
T = √Eo ( 1 - A) /4 = 254 K
= - 18° C
d) The average temperature of Earth is around 15°. But due to the greenhouse effect, there is incoherence between two values. We should also take into account the effects of human energy production, geothermal heat and the Earth's internal heat to arrive at an accurate value.