Water, Air & Weather
Class 11–12 – Environmental Studies / Science
Advanced, MIT‑style treatment from first principles
Prepared for the Arts/Humanities stream, but with full rigor and depth so that students can appreciate the science behind everyday phenomena.
Table of Contents
| # | Section | Key Topics |
|---|---|---|
| 1 | Introduction & Scope | Why water, air and weather matter |
| 2 | The Hydrosphere | Water’s physical properties, phase changes, the global water cycle |
| 3 | The Atmosphere | Composition, structure, thermodynamics, radiative transfer |
| 4 | Atmospheric Dynamics & Weather | Pressure systems, fronts, wind, cyclones, monsoons, climate vs weather |
| 5 | Advanced Theoretical Tools | Thermodynamics, fluid dynamics, radiative transfer, phase‑change equations |
| 6 | Edge Cases & Anthropogenic Impacts | Climate extremes, air‑quality issues, water scarcity, desertification |
| 7 | Challenging Problem | A multi‑step calculation that ties the theory together |
| 8 | Further Reading & References | Suggested texts, papers, and online resources |
Note: All equations are presented in SI units unless otherwise stated.
Notation: Boldface for vectors, ∇ for gradient, ∇· for divergence, ∇× for curl.
1. Introduction & Scope
| Concept | Why it matters for students |
|---|---|
| Water | Life‑supporting resource, economic backbone, cultural significance. |
| Air | Medium for respiration, climate regulation, transport of pollutants. |
| Weather | Daily life (clothes, travel, agriculture), safety (storms, floods). |
2. The Hydrosphere
2.1 Physical Properties of Water
| Property | Value | Significance |
|---|---|---|
| Density (liquid) | 997 kg m⁻³ (at 25 °C) | Defines buoyancy, ocean circulation. |
| Viscosity | 0.89 mPa·s (25 °C) | Affects flow resistance. |
| Surface tension | 72 mN m⁻¹ | Drives capillarity. |
| Heat capacity | 4.18 kJ kg⁻¹ K⁻¹ | Modulates temperature swings. |
| Latent heat of vaporisation | 2.26 MJ kg⁻¹ | Drives evaporation & condensation. |
2.2 Phase Changes & Thermodynamics
-
Clausius–Clapeyron Equation
[ \frac{dP_{!sat}}{dT} = \frac{L_v}{T\Delta V} \quad\Longrightarrow\quad \ln!\left(\frac{P_{!sat}(T)}{P_{!sat}(T_0)}\right) = \frac{L_v}{R_v}!\left(\frac{1}{T_0}-\frac{1}{T}\right) ]
where (L_v) is latent heat, (R_v) the specific gas constant for water vapour.
-
Saturation Mixing Ratio
[ q_s = \frac{\epsilon,e_s}{P-e_s},\quad \epsilon = 0.622 ]
with (e_s) the saturation vapour pressure.
2.3 The Global Water Cycle
| Process | Description | Key Equations |
|---|---|---|
| Evaporation | Liquid → vapour at surface | (E = \rho,c_p,(T_s-T_a)/\Delta z) (simplified heat flux) |
| Condensation | Vapour → liquid | (C = -E) (mass balance) |
| Precipitation | Cloud droplets → rain/snow | (P = C - D) (deposition) |
| Run‑off | Surface flow to streams | (Q = \frac{A,\Delta h}{R}) (Manning’s equation) |
| Infiltration | Groundwater recharge | (f = K_s(1+ \frac{\psi_f}{h})) |
| Groundwater Flow | Darcy’s law | (\mathbf{q} = -K\nabla h) |
Edge case: Super‑critical water (> 374 °C, > 22 MPa) used in industrial processes; behaves as a dense fluid with gas‑like diffusivity.
3. The Atmosphere
3.1 Composition
| Component | Mass % | Molar % | Role |
|---|---|---|---|
| N₂ | 78.08 | 78.09 | Inert |
| O₂ |