Last modified by Gijs Zwartsenberg on 2021/06/11 13:28
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1 # Redundant thermal energy released by nuclear power plants vs. the thermal energy as provided by the sun
2
3 This notebook is a first stab at an approximate calculation to get an idea of the magnitude of the redundant thermal energy that is released by nuclear power plants as compared to that which is supplied by the sun through irridiating Earth.
4
5 ## Calculate the incident infra-red solar energy at the surface of Earth.
6
7 ```python
8 import math
9 ```
10
11 Earth radius in meters is:
12
13 ```python
14 equatorial_radius = 6378e03
15 polar_radius = 6357e03
16 ```
17
18 Approximate Earth surface exposed to solar irradiance can be calculated from  $\pi\cdot r^2$. This can be though of as a disc (plane) facing the sun (i.e. perpendicular to the rays) that is illuminated by sunlight.
19
20 ```python
21 earth_disc_surface = math.pi * equatorial_radius**2
22 print('irradated surface area: ', earth_disc_surface,'m^2')
23 ```
24
25 irradated surface area:  127796483130631.38 m^2
26
27 Sunlight's composition at ground level, per square meter, with the sun at the zenith, is about 527 watts of infrared radiation, 445 watts of visible light, and 32 watts of ultraviolet radiation.
28
29 <https://ag.tennessee.edu/solar/Pages/What%20Is%20Solar%20Energy/Sunlight.aspx>
30
31 ```python
32 infrared_sol_power = 527
33 ```
34
35 Total solar infrared power available at the surface is thus:
36
37 ```python
38 earth_sol_power = earth_disc_surface * infrared_sol_power
39 print('Total power: ',earth_sol_power / 1e12, 'Tera Watt' )
40 print('Total power: ',earth_sol_power / 1e15, 'Peta Watt')
41 ```
42
43 Total power:  67348.74660984274 Tera Watt
44 Total power:  67.34874660984273 Peta Watt
45
46 Total energy delivered over a year is thus:
47
48 ```python
49 earth_sol_energy = earth_sol_power * 24 * 365
50 print('Total energy: ', earth_sol_power * 24 * 365 / 1e18, 'Exa Watt hour' )
51 ```
52
53 Total energy:  589.9750203022223 Exa Watt hour
54
55 ## Calculate the total thermal energy released by all nuclear power plants on Earth
56
57 Nuclear energy now provides about 10% of the world's electricity from about 440 power reactors. In 2018 nuclear plants supplied 2563 TWh of electricity.
58
59 <https://www.world-nuclear.org/information-library/current-and-future-generation/nuclear-power-in-the-world-today.aspx>
60
61 Nuclear power plants usually have efficiency about 33%. In modern nuclear power plants the overall thermodynamic efficiency is about one-third (33%), so 3000 MWth of thermal power from the fission reaction is needed to generate 1000 MWe of electrical power.
62
63 ```python
64 electric_energy = 2563e12
65 efficiency = 0.33
66 thermal_energy = electric_energy / efficiency
67 print('Initial thermal: ', thermal_energy / 1e12, 'Tera Watt hour')
68 ```
69
70 Initial thermal:  7766.666666666666 Tera Watt hour
71
72 ```python
73 released_energy = thermal_energy - electric_energy
74 print('Released thermal: ', released_energy / 1e12, 'Tera Watt hour')
75 ```
76
77 Released thermal:  5203.666666666666 Tera Watt hour
78
79 ## Ratio of solar infrared energy and heat released by nuclear power plants
80
81 ```python
82 ratio = released_energy/earth_sol_energy
83 ```
84
85 The ratio of thermal energy released by all nuclear power plants in the world over the period of a year, to the total delivered thermal energy by the sun over the period of a year is given below.
86
87 ```python
88 print(ratio)
89 ```
90
91 8.82014744285448e-06
92
93 ```python
94
95 ```

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