Unit 1: Fundamentals of environmental physics

Basic concepts of light and matter

In environmental science, we study the interaction between energy and matter. The environment is composed of matter (atoms, molecules, soil, water, air) and is driven by energy, primarily from light (solar radiation).

• Matter: Anything that has mass and takes up space. It exists in various states (solid, liquid, gas, plasma). In the environment, this includes chemical substances like H₂O, CO₂, N₂, O₂, and pollutants like SO₂, Pb, etc.
• Light (Electromagnetic Radiation - EMR): A form of energy that travels in waves. It has a dual nature, behaving as both a wave and a particle (called a photon).

The entire range of EMR is called the Electromagnetic Spectrum. This includes (from high energy/short wavelength to low energy/long wavelength): gamma rays, X-rays, ultraviolet (UV), visible light, infrared (IR), microwaves, and radio waves.

Quantum mechanics

Relation between energy, wavelength and frequency

Quantum mechanics explains that energy is not continuous but comes in discrete packets called quanta (for light, these are photons). The energy of a single photon is directly related to its frequency and inversely related to its wavelength.

Formula 1: Planck's Equation

E = hν

• E = Energy of the photon (in Joules)
• h = Planck's constant (6.626 x 10⁻³⁴ J·s)
• ν (nu) = Frequency of the light (in Hertz, Hz, or s⁻¹)

The frequency and wavelength of light are related by the speed of light (c).

Formula 2: Wave Equation

c = λν

• c = Speed of light (3.0 x 10⁸ m/s)
• λ (lambda) = Wavelength (in meters)
• ν (nu) = Frequency (in Hz)

By combining these two equations (rearranging Formula 2 as ν = c / λ and substituting into Formula 1), we get the most common form used in environmental science:

Formula 3: Energy-Wavelength Relation

E = hc / λ

Black body radiation

A black body is a theoretical, ideal object that absorbs 100% of the radiation that hits it (it doesn't reflect any) and emits radiation perfectly based on its temperature.

While no real object is a perfect black body, the Sun and the Earth are often approximated as black bodies to model the planet's energy budget.

There are two key laws governing black body radiation:

1. Stefan-Boltzmann Law: Describes the total amount of energy an object radiates. It states that the total energy (E) radiated per unit surface area is proportional to the fourth power of its absolute temperature (T, in Kelvin).

   Formula: E = σT⁴ (where σ is the Stefan-Boltzmann constant)

   Implication: A small increase in temperature leads to a large increase in radiated energy. This is a key factor in global warming.

2. Wien's Displacement Law: Describes the peak wavelength (λ_max) of the emitted radiation. It states that the peak wavelength is inversely proportional to the absolute temperature (T).

   Formula: λ_max = b / T (where b is Wien's displacement constant)

Spectroscopic concepts

Introduction to the concept of absorption and transmission of light

When light (a photon) hits a molecule, one of three things can happen:

• Transmission: The light passes straight through the molecule. The material is transparent.
• Reflection/Scattering: The light bounces off the molecule.
• Absorption: The molecule "catches" the photon, and its energy is transferred to the molecule, causing it to move to a higher energy state (e.g., electrons jump to a higher orbital, or the molecule vibrates/rotates faster).

Spectroscopy is the study of how EMR interacts with matter. In environmental chemistry, we use it to identify and quantify substances.

Beer-Lambert Law

The Beer-Lambert Law (or Beer's Law) is a fundamental principle for measuring the concentration of a substance in a solution. It states that the amount of light absorbed by a solution is directly proportional to the concentration of the absorbing substance and the path length of the light through the solution.

Formula: Beer-Lambert Law

A = εcl

• A = Absorbance (unitless, measured by a spectrophotometer)
• ε (epsilon) = Molar absorptivity (a constant specific to the substance at a specific wavelength, in L mol⁻¹ cm⁻¹)
• c = Concentration of the substance (in mol L⁻¹)
• l = Path length of the cuvette (sample holder), usually 1 cm.

Basic concepts of pressure, force, work and energy

• Force (F): A push or a pull on an object. Measured in Newtons (N). (F = mass × acceleration).
  Example: The force of wind on a turbine, or the force of gravity pulling rain down.
• Pressure (P): The amount of force applied over a specific area (P = Force / Area). Measured in Pascals (Pa) or atmospheres (atm).
  Example: Atmospheric pressure is the weight (force) of the entire column of air above you, pressing down on the surface (area). Hydrostatic pressure is the pressure exerted by a fluid (like water) at a certain depth.
• Work (W): Done when a force causes an object to move a certain distance (W = Force × Distance). Measured in Joules (J).
  Example: A river (water) does work when it applies a force to erode sediment and move it (distance) downstream.
• Energy (E): The capacity or ability to do work. Measured in Joules (J).
  Forms: Kinetic energy (energy of motion, e.g., wind, flowing water) and Potential energy (stored energy, e.g., water stored behind a dam, chemical energy stored in wood or biomass).

Laws of thermodynamics

Thermodynamics is the study of energy, its transformations, and its relationship to matter. These laws are fundamental to understanding energy flow in ecosystems.

First Law of Thermodynamics (Law of Conservation of Energy)

"Energy cannot be created or destroyed, only changed from one form to another."

Ecological Implication: All energy in an ecosystem must be accounted for. The total energy from the sun that is captured by plants (producers) is either:

• Converted into chemical energy (biomass) by the plant.
• Transferred to an animal that eats the plant (herbivore).
• Lost as heat during respiration.

This law explains the flow of energy through a food web.

Second Law of Thermodynamics (Law of Entropy)

"In any energy conversion, some energy is converted to a less useful form (usually heat), and the total disorder (entropy) of the system increases."

This means no energy transfer is 100% efficient.
Ecological Implication: This is the most important law in ecology. It explains:

• The 10% Rule: When a herbivore eats a plant, only about 10% of the plant's energy is converted into herbivore biomass. The other 90% is "lost" as heat during metabolism, movement, and waste.
• Ecological Pyramids: Because so much energy is lost at each step, there is progressively less energy and biomass at higher trophic levels (e.g., more grass than zebras, and more zebras than lions). This is why food chains are rarely longer than 4-5 levels.