1.0 Environmental Physics

Definition: Environmental physics is an interdisciplinary field integrating physical processes in the Atmosphere, Biosphere, Hydrosphere, and Geosphere. It studies the response of living organisms to their environment.

The environment is structured within the relationship between:

  • Atmosphere: The gaseous envelope surrounding the Earth.
  • Hydrosphere: All water bodies including oceans, rivers, and groundwater.
  • Lithosphere (Geosphere): The solid Earth, rocks, and soil.
  • Biosphere: The zone where life exists, interacting with all other spheres.

1.1 Agriculture Physics

Agriculture physics applies physical principles to soil, plant, and atmospheric systems to optimize food production.

Photosynthetically Active Radiation (PAR): Plants utilize light in the 400-700 nm range. The intensity of radiation determines the rate of photosynthesis.
  • Phototropism: Growth towards light.
  • Photoperiodism: Response to the length of day/night cycles (flowering).

  • Wind: Increases transpiration rate by removing the boundary layer of saturated air from leaves. Mechanical stress from wind also strengthens stems (thigmomorphogenesis).
  • Air Temperature: Dictates the rate of biochemical reactions (enzyme activity). Every plant has a minimum, optimum, and maximum temperature for growth ($T_{min}, T_{opt}, T_{max}$).
  • Rainfall: Provides water for turgidity, nutrient transport, and photosynthesis electrons.

Soil physics deals with the physical properties of soil that influence plant growth:

  • Soil Texture & Structure: Determines porosity and aeration.
  • Soil Water Potential: Governs how easily plants can extract water.
  • Thermal Properties: Soil heat capacity controls how fast soil warms up in spring. Dark soils absorb more heat than light soils (Albedo effect).

1.2 Human Survival Physics

Humans are homeotherms, maintaining a relatively constant body temperature (~37°C) despite environmental changes. Physics governs this thermal regulation.

The Energy Balance Equation

$$ S = M – W \pm R \pm C – E $$

\(S\) = Heat storage rate (W)
\(M\) = Metabolic rate (Heat production)
\(W\) = Mechanical work done by the body
\(R\) = Radiation heat exchange
\(C\) = Convection heat exchange
\(E\) = Evaporation heat loss (Sweating)

Heat Exchange Mechanisms

  • Metabolism ($M$): The biochemical process of converting food into energy. Basal Metabolic Rate (BMR) is the energy required at rest.
  • Radiation ($R$): Transfer of heat via electromagnetic waves. Depends on the temperature difference between skin and surroundings ($R \propto T_{skin}^4 – T_{env}^4$).
  • Convection ($C$): Heat loss to air or water moving across the skin. Wind chill factor increases convection loss.
  • Evaporation ($E$): The most effective cooling mechanism in hot environments. Latent heat of vaporization ($L_v$) removes heat as sweat turns to vapor.

1.3 Energy from the Environment

Renewable energy physics focuses on converting natural energy flows into useful work.

Photovoltaic (PV)

Converts photon energy ($E=hf$) into electrical current using PN-junction semiconductors. Efficiency depends on band-gap energy and temperature.

Wind Power

Power extracted is proportional to the cube of wind speed: $$ P = \frac{1}{2} \rho A v^3 $$ where $\rho$ is air density and $A$ is rotor area.

Geothermal

Utilizes radioactive decay heat from the Earth’s core. Operates via steam turbines driven by hydrothermal reservoirs.

Wave Energy

Captures kinetic and potential energy of ocean waves. Wave power density depends on wave height squared ($H^2$) and period ($T$).

1.4 Built Environment & Remote Sensing

The Built Environment

Physics applied to human-made structures. Key concepts involve heat transfer and comfort.

  • Thermal Comfort: Dependent on air temperature, radiant temperature, humidity, and air velocity.
  • U-Value: Measure of thermal transmittance through walls. Lower U-values mean better insulation ($Rate = U \cdot A \cdot \Delta T$).
  • Natural Ventilation: Using pressure differences caused by wind (Bernoulli’s principle) and stack effect (warm air rising) to cool buildings.

Remote Sensing

The acquisition of information about an object without making physical contact, typically via satellite or aircraft.

Physics Principle: It relies on the detection of Electromagnetic Radiation (EMR) reflected or emitted from the Earth’s surface. Different surfaces (water, soil, vegetation) have distinct Spectral Signatures.
  • Active Sensors: Emit their own energy (e.g., Radar, LiDAR).
  • Passive Sensors: Detect natural energy (Sunlight) reflected (e.g., Photography, Landsat).

1.6 Geophysics (Seismology)

Seismology is the study of earthquakes and the propagation of elastic waves through the Earth.

Elastic Rebound Theory

Explains earthquake generation: Tectonic forces deform rocks. When stress exceeds rock strength, rupture occurs, and rocks “rebound” to an unstrained position, releasing energy as seismic waves.

Seismic Waves Classification

Type Name Nature Characteristics
Body P-Waves Longitudinal Fastest ($~8 km/s$). Pass through solids, liquids, gases.
Body S-Waves Transverse Slower ($~4.5 km/s$). Cannot pass through liquids (Outer Core).
Surface L-Waves Complex Slowest. Travel along surface. Cause most structural damage.
Shadow Zones: The S-wave shadow zone (103° to 103°) provides the primary evidence that the Earth’s Outer Core is liquid, as S-waves cannot penetrate it.

1.7 Environmental Pollution

Transport Mechanisms

How pollutants move in the atmosphere:

  • Advection: Horizontal transport of pollutants by wind.
  • Diffusion: Spreading of pollutants from high to low concentration due to turbulence.
  • Deposition: Removal of pollutants via rain (Wet deposition) or gravity (Dry deposition).

Optical Properties & Visibility

Pollution affects how light travels through the atmosphere, reducing visibility.

  • Scattering: Particulates (aerosols) scatter light. Mie Scattering occurs when particles are similar in size to the wavelength of light (causing white smog). Rayleigh Scattering affects smaller molecules (blue sky).
  • Absorption: Some pollutants (like soot or $NO_2$) absorb light, causing dark smoke or brownish haze.

Nuclear Waste

Radioactive waste management involves shielding and isolation.

  • High-Level Waste (HLW): Spent fuel. Requires cooling and deep geological disposal.
  • Half-life ($T_{1/2}$): The time taken for radioactivity to drop to half. Waste must be stored for multiple half-lives.

2.0 Current Electricity

2.1 Drift Velocity Theory

In a conductor, free electrons move randomly. When an electric field $E$ is applied, they acquire a slow average velocity component called Drift Velocity ($v_d$).

Derivation of \(I = nAve\)

  1. Consider a conductor of length \(L\) and cross-sectional area \(A\).
  2. Volume of the conductor \(V = A \times L\).
  3. If \(n\) is the number of free electrons per unit volume, total number of electrons \(N = n \times (AL)\).
  4. Total Charge \(Q = N \times e = nALe\).
  5. Time taken for charge to cross length \(L\) with velocity \(v_d\) is \(t = \frac{L}{v_d}\).
  6. Current \(I = \frac{Q}{t} = \frac{nALe}{L/v_d} = nAev_d\).
Drift Velocity Equation

$$ I = n A v_d e $$

\(I\) = Current (A)
\(n\) = Charge carrier density ($m^{-3}$)
\(A\) = Cross-sectional Area ($m^2$)
\(v_d\) = Drift Velocity ($m/s$)
\(e\) = Electronic charge ($1.6 \times 10^{-19} C$)

2.2 Current Density ($J$)

Current density is a vector quantity defined as the current per unit area.

$$ J = \frac{I}{A} = n v_d e $$

Vector Form (Microscopic Ohm’s Law): $$ J = \sigma E $$

Where $\sigma$ is Conductivity and $E$ is Electric Field intensity.

2.3 Resistance & Resistivity

Resistance ($R$) opposes current flow. It depends on geometry and material properties.

$$ R = \rho \frac{L}{A} $$

  • $\rho$ (Rho): Resistivity ($\Omega m$). Intrinsic property of material.
  • $L$: Length of conductor.
  • $A$: Cross-sectional area.
  • Conductivity ($\sigma$): Reciprocal of resistivity ($\sigma = 1/\rho$).

2.4 Temperature Coefficient of Resistance

For metallic conductors, resistance increases with temperature.

Formula: $$ R_\theta = R_0 (1 + \alpha \Delta \theta) $$
Where:
$R_\theta$ = Resistance at temp $\theta$
$R_0$ = Resistance at $0^\circ C$
$\alpha$ = Temperature coefficient of resistance ($K^{-1}$ or $^\circ C^{-1}$)

Lab: Drift Velocity Calculator

Calculate the drift velocity of electrons in a wire using the formula \(v_d = I / (nAe)\).

Copper approx: \(8.4 \times 10^{28}\)

ACSEE Practice Problems

Question: Calculate the drift velocity in a silver wire of area \(4.5 \times 10^{-6} m^2\) carrying 5 A. ($n = 5.8 \times 10^{28} m^{-3}$).

Solution:
\(v_d = \frac{I}{nAe} = \frac{5}{(5.8 \times 10^{28})(4.5 \times 10^{-6})(1.6 \times 10^{-19})}\)
\(v_d = \frac{5}{41.76 \times 10^{3}} \approx 1.2 \times 10^{-4} m/s\)

Question: A wire of length 2.0 m and diameter 0.4 mm has a resistance of 2.5 $\Omega$. Calculate its resistivity.

Solution:
1. Area $A = \pi r^2 = \pi (0.2 \times 10^{-3})^2 = 1.257 \times 10^{-7} m^2$
2. Formula $R = \rho L / A \Rightarrow \rho = RA/L$
3. $\rho = (2.5 \times 1.257 \times 10^{-7}) / 2.0$
4. $\rho = 1.57 \times 10^{-7} \Omega m$

Question: A coil has a resistance of 10 $\Omega$ at $0^\circ C$ and 15 $\Omega$ at $100^\circ C$. Find $\alpha$.

Solution:
$R_{100} = R_0(1 + \alpha \Delta T)$
$15 = 10(1 + \alpha \cdot 100)$
$1.5 = 1 + 100\alpha \Rightarrow 0.5 = 100\alpha$
$\alpha = 0.005 K^{-1}$
Physics Form 6 Notes | Based on Tanzania ACSEE Syllabus | © 2025 Physics Master