DP IB Physics: SL

B. The particulate nature of matter

B.2 Greenhouse effect

DP IB Physics: SL B. The particulate nature of matter B.2 Greenhouse effect Understandings Students should understand:
a)	The conservation of energy
b)	Emissivity as the ratio of the power radiated per unit area by a surface compared to that of an ideal black surface at the same temperature as given by [math]\varepsilon = \frac{\text{power radiated per unit area}}{\sigma T^4}[/math]
c)	Albedo as a measure of the average energy reflected off a macroscopic system as given by [math]\alpha = \frac{\text{total scattered power}}{\text{total incident power}}[/math]
d)	That Earth’s albedo varies daily and is dependent on cloud formations and latitude
e)	The solar constant S
f)	That the incoming radiative power is dependent on the projected surface of a planet along the direction of the path of the rays, resulting in a mean value of the incoming intensity being [math]\frac{S}{4}[/math]
g)	That methane CH₄, water vapour H₂O, carbon dioxide CO₂, and nitrous oxide N₂O, are the main greenhouse gases and each of these has origins that are both natural and created by human activity
h)	The absorption of infrared radiation by the main greenhouse gases in terms of the molecular energy levels and the subsequent emission of radiation in all directions
i)	That the greenhouse effect can be explained in terms of both a resonance model and molecular energy levels
j)	That the augmentation of the greenhouse effect due to human activities is known as the enhanced greenhouse effect.

a) The Principle of Conservation of Energy:
The principle of conservation of energy states that energy cannot be created or destroyed, only transformed from one form to another or transferred between objects.
Total Energy Initial = Total Energy Final
1. In a closed system, the total energy remains constant.
2. Energy can change forms:
– Kinetic energy
[math]E_k = \frac{1}{2} mv^2[/math]
– Potential energy (gravitational)
[math]E_p = mgh[/math]
– Thermal energy, electrical energy, etc.
1. In real-world systems, some energy is often converted into heat due to friction or resistance, but total energy is still conserved.
Figure 1 Law of conservation of energy
⇒ Examples of Energy Conservation:
1. Pendulum Motion:
– At the highest point, maximum potential energy.
– At the lowest point, maximum kinetic energy.
– Ignoring air resistance, total mechanical energy remains constant.
2. Roller Coaster:
– At the top: High gravitational potential energy.
– As it descends: Potential energy converts to kinetic energy.
– Without friction, the sum of kinetic and potential energy remains constant.
3. Energy in Space (Solar Radiation):
– The Sun emits energy in the form of radiation.
– Planets absorb, reflect, and re-radiate energy, following conservation principles.
b) Emissivity and Black Body Radiation
⇒ Emissivity (ε)
Emissivity measures how efficiently a surface emits thermal radiation compared to an ideal black body.
[math]\varepsilon = \frac{\text{power radiated per unit area}}{\sigma T^4}[/math]
Where:
– σ = 67 × 10⁻⁸Wm⁻²K⁻⁴ is the Stefan-Boltzmann constant.
– T is the absolute temperature in Kelvin (K).
– A black body has ε=1 (perfect emitter).
– Real objects have .
⇒ Properties of Emissivity:
– Dark, rough surfaces (e.g., charcoal, black paint) have high emissivity (~0.95-1).
– Light, shiny, or reflective surfaces (e.g., polished metal, snow) have low emissivity (~0.1-0.3).
⇒ Example: The Earth and Radiation
– The Earth absorbs solar radiation and emits infrared radiation.
– Different surfaces (ocean, deserts, forests) have different emissivity values, affecting temperature regulation.
c) Albedo and Reflectivity
Albedo is the fraction of total incident energy that is reflected by a surface.
[math]\text{Albedo} = \frac{\text{total scattered power}}{\text{total incident power}}[/math]
Albedo ranges from 0 to 1:
– 0 → Perfect absorber (e.g., black hole, deep ocean).
– 1 → Perfect reflector (e.g., fresh snow, mirror).
⇒ Examples of Albedo:

Surface	Albedo Value
Fresh Snow	~0.8-0.9
Desert Sand	~0.4-0.6
Water (Ocean)	~0.1-0.3
Forest	~0.1-0.2
Asphalt	~0.05-0.15

⇒ Importance of Albedo in Climate Science:
1. Earth’s Energy Balance:
– High albedo (snow, ice) → More reflection, cooling effect.
– Low albedo (forests, oceans) → More absorption, warming effect.
2. Global Warming & Ice Melting:
– Melting ice lowers Earth’s albedo, causing more energy absorption.
– More heat absorption leads to more warming, creating a positive feedback loop.
Figure 2 Emissivity
d) Earth’s Albedo and Its Variability
Albedo (α) is the fraction of total incoming solar radiation that is reflected by Earth’s surface and atmosphere.
[math]\alpha = \frac{\text{Total Scattered (Reflected) Power}}{\text{Total Incident Power}}[/math]
– It is expressed as a decimal or percentage (e.g., 0.3 or 30%).
– A higher albedo means more radiation is reflected, while a lower albedo means more radiation is absorbed.
Figure 3 Earth’s Albedo effect the global Warming
⇒ Daily Variation of Albedo:
Earth’s albedo changes throughout the day due to:
1. Cloud Cover:
– Thick clouds reflect more sunlight, increasing albedo.
– Clear skies reduce reflection, decreasing albedo.
2. Latitude & Angle of Sunlight:
– At the poles (high latitude), more reflection occurs due to ice and snow.
– At the equator, the ocean and forests absorb more sunlight, lowering albedo.
3. Seasons & Snow/Ice Cover:
– Winter: More snow, higher albedo.
– Summer: Less snow, lower albedo.
4. Urbanization & Deforestation:
– Deforestation (removal of dark forests) → higher albedo.
– Urban areas (concrete, asphalt) absorb more heat → lower albedo.
⇒ Typical Albedo Values for Different Surfaces:

Surface Type	Albedo Value
Fresh Snow	0.8 – 0.9
Thick Clouds	0.6 – 0.8
Desert Sand	0.3 – 0.5
Forests	0.1 – 0.2
Water (Ocean)	0.05 – 0.3
Asphalt	0.05 – 0.15

Earth’s average albedo is about 3 (30%), meaning 30% of sunlight is reflected, and 70% is absorbed.
⇒ Importance of Albedo in Climate Change:
Melting ice decreases albedo → more heat absorption → warmer temperatures → positive feedback loop.
Increased cloud cover may either increase or decrease albedo, depending on cloud type.
e) The Solar Constant (S)
The solar constant (S) is the amount of solar energy per unit area received at the top of Earth’s atmosphere, perpendicular to the Sun’s rays.
[math]S = 1361W/m^2[/math]
Measured at 1 astronomical unit (AU) (the average distance between Earth and the Sun: ~ 5 × 10⁸ km).
Varies slightly due to the Earth’s elliptical orbit.
Figure 4 Solar radiation
⇒ Factors Affecting S:
1. Sun’s Activity:
– More sunspots → Higher S (solar maximum).
– Fewer sunspots → Lower S (solar minimum).
2. Distance from the Sun:
– Closer planets (e.g., Mercury) receive a higher
– Farther planets (e.g., Mars) receive a lower S.
⇒ Examples of Solar Constants for Other Planets:

Planet	Distance from Sun (AU)	Solar Constant (S) (W/m²)
Mercury	0.39 AU	~9,100 W/m²
Venus	0.72 AU	~2,600 W/m²
Earth	1.00 AU	~1,361 W/m²
Mars	1.52 AU	~590 W/m²
Jupiter	5.20 AU	~50 W/m²

f) Incoming Radiative Power and Mean Intensity (S/2)
⇒ Projected Surface Area and Incoming Power
The solar constant (S) represents the power per unit area received at the top of Earth’s atmosphere on a surface perpendicular to the Sun’s rays.
However, Earth is a sphere and sunlight spreads over the entire surface.
1. The Earth’s cross-sectional area exposed to sunlight is:
[math]A_{perpendicular} = πR^2[/math]
2. The total surface area of the Earth (a sphere) is:
[math]A_{total} = 4πR^2[/math]
3. Since the sunlight spreads over the entire surface, the average intensity received per unit area is:
[math]I_{average} = \frac{S}{4}[/math]
⇒ Numerical Calculation for Earth:
[math]I_{average} = \frac{S}{4} \\ I_{average} = \frac{1361}{4} ≈ 340.25 W/m^2[/math]
This means that, on average, the Earth’s surface receives about 340 W/m² of solar energy.
S applies to a surface perpendicular to the Sun’s rays.
Earth’s curvature spreads sunlight over a larger area, reducing the mean solar intensity to S/2.
This is crucial for climate models, as it helps determine Earth’s energy balance and temperature.
g) Main Greenhouse Gases and Their Origins
Greenhouse gases (GHGs) are atmospheric gases that absorb and emit infrared radiation, leading to the greenhouse effect. The primary greenhouse gases include:
(a) Methane (CH₄)
Natural Sources: Wetlands, termites, oceanic methane release.
Human Sources: Agriculture (rice paddies, livestock digestion), landfills, fossil fuel extraction (natural gas leaks), biomass burning.
(b) Water Vapor (H₂O)
Natural Sources: Evaporation from oceans, lakes, and rivers; transpiration from plants.
Human Influence: Indirectly increased due to global warming, as higher temperatures enhance evaporation.
(c) Carbon Dioxide (CO₂)
Natural Sources: Volcanic eruptions, respiration by living organisms, decomposition of organic matter.
Human Sources: Burning fossil fuels (coal, oil, natural gas), deforestation, cement production.
(d) Nitrous Oxide (N₂O)
Natural Sources: Soil bacteria processes (denitrification), ocean emissions.
Human Sources: Fertilizer use, combustion engines, industrial activities, biomass burning.
Figure 5 Climate Science investigations
h) Absorption of Infrared Radiation by Greenhouse Gases
Greenhouse gases absorb infrared radiation emitted by the Earth’s surface due to their molecular structure. Each molecule has specific energy levels, allowing it to absorb radiation at particular wavelengths.
Working:
1. Molecular Vibrations: Greenhouse gas molecules absorb infrared photons, increasing their vibrational energy.
2. Emission in All Directions: After absorbing energy, the molecules re-emit infrared radiation, some of which returns to Earth, trapping heat.
3. Spectral Absorption: Different gases absorb radiation at different infrared wavelengths.
– CO₂ absorbs strongly at 15 μm.
– CH₄ absorbs in the 3–8 μm range.
– H₂O absorbs across a broad range of infrared wavelengths.
– N₂O absorbs around 4.5 μm and 7.8 μm.
This trapping and re-emission of infrared radiation maintains the Earth’s temperature above what it would be without an atmosphere.
Figure 6 Greenhouse effect
i) Explanation of the Greenhouse Effect in Terms of Resonance and Molecular Energy Levels
(a) Resonance Model
When infrared radiation of a particular frequency interacts with a greenhouse gas molecule, if the frequency of the radiation matches the natural vibrational frequency of the molecule, resonance occurs.
This excites the molecule, increasing its vibrational energy and allowing it to absorb and store heat.
(b) Molecular Energy Levels
Molecules have quantized energy levels related to vibration, rotation, and electronic states.
Infrared absorption excites molecular bonds, moving them to higher vibrational states.
When molecules return to a lower energy state, they emit radiation, which may be sent back toward Earth’s surface, leading to warming.
This process creates a thermal equilibrium where energy input from the Sun equals the heat lost to space, maintaining the Earth’s climate.
Figure 7 Greenhouse in term of molecular energy level
j) The Enhanced Greenhouse Effect Due to Human Activity
(a) The Enhanced Greenhouse Effect:
Human activities, such as burning fossil fuels and deforestation, have increased the concentration of greenhouse gases.
This leads to additional heat retention, causing global warming.
(b) Consequences of the Enhanced Greenhouse Effect:
Rising Global Temperatures: Increased trapped heat raises Earth’s surface temperature.
Climate Change: Altered weather patterns, more extreme weather events.
Ice Melt & Sea-Level Rise: Polar ice caps and glaciers melt, increasing ocean levels.
Ocean Acidification: Higher CO₂ levels dissolve into oceans, lowering pH and harming marine life.
Disruption of Ecosystems: Changes in temperature and precipitation affect plant and animal survival.
(c) Evidence of the Enhanced Greenhouse Effect:
Historical CO₂ Measurements: Ice core samples show CO₂ levels are at their highest in over 800,000 years.
Temperature Records: Global temperatures have risen approximately 2°C since pre-industrial times.
Glacier and Polar Ice Loss: Arctic ice has significantly declined in extent.
Figure 8 Enhance greenhouse effect due to human activity