TB: The Physics of Climate Change (Krauss)

• Life likely began by harvesting energy from Earth's core, then discovered a vastly richer source: sunlight at the surface supplies roughly 10⁵× the geothermal energy available at the crust.
• Respiration is controlled burning. Breathing and combustion both combine O₂ with organic compounds to yield CO₂. By routing electrons in O₂ → ATP, living systems extract ~30× the energy they would obtain from photosynthesis alone. Biology is already a carbon-combustion engine; the industrial revolution is the same chemistry at a different scale.
• Human impact turns on a time asymmetry: we access in ~2 centuries a reservoir of carbon that took ~10⁸ years to accumulate — fossil fuels are sunlight integrated over geological time and discharged in an eye-blink. This is what "ushered in modernity."
• Generalizing: Huge reservoirs of easy-to-use energy may be a precondition for advanced civilization anywhere. (See also Physics of Energy.)

• The solar constant at Earth's orbital distance is ~1 kW/m² at a plane normal to the Sun. Distributed over the rotating sphere (πR² intercepted ÷ 4πR² surface) yields ~0.3 kW/m² average insolation.
• Integrated, solar flux is roughly 1000× total human energy consumption — the resource asymmetry is not the problem; storage, conversion, and density are.
• The greenhouse effect is not symmetric in altitude. Most incoming sunlight is absorbed at the surface, where it is warm. Most outgoing IR escapes from the top of the atmosphere, which is cold and carries a higher CO₂ mole fraction. Radiation from the top-of-atmosphere is what the universe sees, and adding CO₂ there is what shifts the balance. The subtlety is that the radiating layer's altitude (and therefore temperature) changes with CO₂, not the surface properties directly.

• A diatomic homonuclear molecule (N₂, O₂) has only one vibrational mode — symmetric stretch — and no permanent or changing dipole moment in that mode. It does not couple to the IR photon field at climate-relevant frequencies.
• Triatomic molecules (CO₂, H₂O) have bending modes. Bending is slower than stretching and falls squarely in the IR. CO₂'s asymmetric stretch and bend both modulate the dipole; H₂O is permanently polar.

O=C=O           O
               / \
bend →        H   H
               bend →

• N₂ and O₂ therefore absorb preferentially in the UV (blocking harmful high-energy photons) while CO₂ and H₂O absorb in the IR (trapping thermal radiation). The same accident of molecular physics that keeps the atmosphere transparent to visible sunlight is what makes trace gases dominate the outgoing IR budget.

A clean exercise in Estimation:

• CO₂ is ~0.03% by volume, ~0.05% by mass of the atmosphere.
• Atmospheric column mass ≈ 10⁴ kg/m² (~10 tons/m²).
• CO₂ column mass: 5×10⁻⁴ × 10⁴ kg/m² ≈ 5 kg/m² (~0.5 g/cm²).
• Partial pressure: ~0.3 mm Hg.
• Organic-density column height: ρ_C ≈ ρ_H₂O ≈ 1 g/cm³ ⇒ if all atmospheric CO₂ were condensed to solid carbon, it would form a layer ~0.5 cm thick over Earth's surface.
• That half-centimeter layer, distributed as a 10⁻⁴ mole fraction, is what determines the planet's radiative balance. The sensitivity of climate to changes in a 10⁻⁴ concentration "naively seems absurd" — until you see that what matters is not the bulk but the opacity it adds to the outgoing IR, for a narrow set of spectral bands, at the coldest altitudes.

• Preindustrial atmospheric carbon: ~600 Gt C. Human additions to date: ~500 Gt C. The system is not perturbed by small amounts.
• Only about half of emitted CO₂ remains airborne; the other half is absorbed by oceans and soils. This airborne fraction is the operative quantity for concentration projections — and it is not a law of nature. It depends on ocean chemistry, biosphere state, and temperature, and may well change under the very warming it is moderating.