Notes: Energy and Heat Transfer in the Atmosphere

Forms of Energy in the Atmosphere

Main forms of energy in the atmosphere are:
- Gravitational-potential energy (PE) due to gravity
- Kinetic energy (KE) from motion
- Internal kinetic energy (temperature)
- Latent energy associated with phase transitions (e.g., ice → water → water vapor)
- Radiant Energy (warming from the Sun)

Gravitational Potential Energy (PE)

PE = m g h
- m = mass of object
- g = acceleration due to gravity = 9.8 m s⁻²
- h = height above ground
Higher/more massive objects have more PE energy

Kinetic Energy (KE)

KE = KE = \tfrac{1}{2} m v^{2}
- v = velocity
KE represents the energy of motion
Example: Wind farms convert the wind’s kinetic energy into electrical energy

Temperature and KE

Temperature is directly related to the average kinetic energy of air molecules in a volume
- Higher mean KE → higher temperature
- Lower mean KE → lower temperature
Cold air: molecules move slowly and are more dense
Warm air: molecules move faster and are less dense
Result: Density differences drive convection (cold, dense air sinks; warm, less dense air rises)

Heat Capacity and Specific Heat

Heat: energy transferred from one object to another due to temperature difference
Heat Capacity (for a given object):
- Ratio of the amount of heat energy absorbed to its temperature rise
- Example (from transcript): if it takes 10 calories to raise the temperature of a glass of water by $2^{\circ}\mathrm{C}$, then the heat capacity is
  \text{Heat Capacity} = \frac{10\ \text{cal}}{2\ \mathrm{^{\circ}C}} = 5\ \text{cal per }^{\circ}\mathrm{C}
Specific Heat (per unit mass):
- Heat capacity per unit mass
- Example: it takes 1 cal to raise the temperature of 1 g of water by 1°C
  \text{Specific heat of water} = 1\ \frac{\text{cal}}{\text{g} \cdot \mathrm{^{\circ}C}}

Why Specific Heat Matters: Sea Breeze

Differences in specific heat between land and water drive sea breeze
- Which material warms more with the same added heat? (land vs water)
- In practice, water has a higher heat capacity per unit mass than dry land, so land heats up/cools down more quickly than the sea
The general relation for heat transfer is: Q = c \, m \, \Delta T
- Q = heat added or removed
- c = specific heat
- m = mass
- \Delta T = change in temperature

Latent Energy (Latent Heat)

Latent heat is the energy required to change the phase of a substance at a constant temperature, either absorbed or released
Why it matters: phase changes in the atmosphere (e.g., evaporation, condensation) involve large energy transfers without a change in temperature
Phase changes and latent heats:
- Liquid → Vapor: latent heat of evaporation (taken/absorbed)
- Vapor → Liquid: latent heat of condensation (released)
- Liquid → Ice: latent heat of freezing (released)
- Ice → Liquid: latent heat of melting (taken)
- Ice → Vapor: latent heat of sublimation (taken)
- Vapor → Ice: latent heat of deposition (released)

Is latent heat a big deal in the atmosphere?

Yes, latent heating is a key mechanism of heat transfer in the atmosphere, alongside conduction, convection, and radiation
Heat transfer mechanisms include:
- Conduction
- Convection
- Radiation
- Latent Heating (phase changes)

Heat Transfer: Conduction

Definition: heat transfer through direct molecular contact
Involves transfer from warm (high energy) to cold (low energy) regions
Larger temperature difference → faster transfer
Atmosphere is not a good conductor of heat (compared to metals) – conduction is relatively inefficient for long-range atmospheric heat transport
Analogy (from transcript): metal rod is an efficient conductor; air is not

Heat Transfer: Convection

Definition: transfer of heat through vertical mass movement of a fluid (liquid or gas)
Warmer, less dense fluid parcels rise; cooler, more dense parcels sink
Atmospheric convection is the process that drives vertical heat transport
The atmosphere often forms thermals (hot air near the surface rising) and generates turbulent motion near the ground
Convection is more efficient than conduction for transporting heat over longer distances

Atmospheric Convection and Thermals

Near the surface, a thin layer is heated by direct contact with the hot surface
A hot, buoyant parcel rises, forming a thermal
Thermals create turbulent motion and can lead to cloud formation
If moisture is enough, vigorous convection can form clouds and thunderstorms (convection often referred to as convection when thunderstorms form)

Radiative Energy and Radiation Basics

Radiant energy (radiation) is energy transferred through electromagnetic waves
Example: the Sun warms your face
Radiation is transmitted via electromagnetic waves that have wavelengths and amplitudes
All objects with temperature > 0 K emit radiation

Wavelengths and Types of Radiation

Types (from the transcript’s chart):
- Radio waves (AM, TV) – longest wavelengths
- Microwaves
- Infrared (IR)
- Visible light
- Ultraviolet (UV)
- X-rays – shortest wavelengths
Each type carries energy per photon and has characteristic wavelengths
In atmosphere, solar radiation spans short wavelengths; terrestrial radiation peaks in the infrared

Stefan-Boltzmann Law (Emission from a Body)

The total radiant energy per unit area emitted by a body is proportional to the fourth power of its absolute temperature:

E = \sigma \; T^{4}

The Stefan-Boltzmann constant: \sigma = 5.67 \times 10^{-8}\ \mathrm{W\,m^{-2}\,K^{-4}}
Consequences:
- Warmer temperatures emit significantly more radiation
- Doubling temperature multiplies emission by 16 (since E ∝ T⁴)

Sun vs Earth Radiation

Sun’s surface temperature ~ 6000 K
- Emitted radiative flux per unit area: E_{\odot} = \sigma (6000\ \text{K})^{4} \approx 7.3 \times 10^{7}\ \mathrm{W\,m^{-2}}
Earth’s effective radiating temperature ~ 288 K
- Emitted flux: E_{\oplus} = \sigma (288\ \text{K})^{4} \approx 390\ \mathrm{W\,m^{-2}}

Wien’s Law

The peak wavelength of emission shifts with temperature:
\lambda_{\max} = \frac{b}{T}
For a blackbody, the peak shifts to shorter wavelengths at higher temperatures
Sun (hot, ~6000 K) peaks in the visible range; Earth (cooler, ~288 K) peaks in the infrared
Wien’s constant: b \approx 2.897 \times 10^{-3}\ \mathrm{m\,K}

Blackbody vs Real Atmosphere: Selective Absorption

Blackbody: idealized perfect absorber and emitter following Stefan-Boltzmann and Wien without modification
Is the atmosphere a blackbody? No
Atmosphere selectively absorbs longwave (infrared) radiation, but does not absorb much of the shortwave solar radiation
Kirchhoff’s Law: an object that selectively absorbs radiation at a particular wavelength tends to re-emit radiation at the same wavelength
Snow: strong infrared absorber but appears white in visible (local selective absorption)

Radiation Processes in the Atmosphere

Emission: object emits radiation as a function of its temperature
Absorption: radiation is absorbed by atmospheric constituents (e.g., H2O, CO₂)
Reflection: some radiation is reflected by surfaces or clouds
Scattering: radiation is redirected by molecules or particles
Transmission: portion of radiation passes through without interaction
In atmospheric context, absorption and emission by water vapor (H2O) and carbon dioxide (CO₂) are particularly important for greenhouse warming

Putting It All Together: Summary Diagram of Heat Transfer

Solar radiation heats the surface
The surface transfers heat to the atmosphere via conduction and convection
Latent heat is released or absorbed during phase changes of atmospheric moisture (e.g., evaporation, condensation)
Convection and latent heat contribute to vertical heat transport and weather formation
Infrared radiation is emitted by Earth and atmosphere; some of this radiation is absorbed and re-emitted by greenhouse gases, contributing to the greenhouse effect
Reflection, absorption, emission, and scattering all occur across multiple components (H2O, CO₂, clouds, surface type)

Summary of Heat Transfer Mechanisms

Conduction: heat transfer through molecular motions from warm to cold regions; stronger with larger temperature differences
Convection: vertical transport via mass movement of a fluid (air or water); dominant in the atmosphere for vertical heat transport
Radiation: energy transfer via electromagnetic waves; includes emission, absorption, reflection, scattering, and transmission
Latent Heating: energy exchange during phase changes of water (evaporation, condensation, freezing, melting, sublimation, deposition)

Practical Atmospheric Implications and Examples

Thermals and convection cells drive cloud formation and thunderstorms when moisture is sufficient
Sea breeze arises from the different specific heats of land and sea; land heats/cools faster than water leading to surface pressure differences and onshore flow
Thunderstorms are often tied to vigorous convection and latent heat release

Quick Reference: Key Equations

Gravitational potential energy: PE = m g h
Kinetic energy: KE = \tfrac{1}{2} m v^{2}
Heat transfer (specific heat): Q = c \; m \; \Delta T
Stefan-Boltzmann law: E = \sigma \; T^{4}, \quad \sigma = 5.67 \times 10^{-8}\ \mathrm{W\,m^{-2}\,K^{-4}}
Emitted power comparison between Sun and Earth:
- Sun: E_{\odot} \approx 7.3 \times 10^{7}\ \mathrm{W\,m^{-2}} at T = 6000 K
- Earth: E_{\oplus} \approx 390\ \mathrm{W\,m^{-2}} at T = 288 K
Wien’s Law: \lambda_{\max} = \frac{b}{T}, \quad b \approx 2.897 \times 10^{-3}\ \mathrm{m\,K}

Notes on Real-World Relevance

Understanding energy forms helps explain weather patterns and atmospheric dynamics
Specific heat differences explain coastal climate phenomena (sea breeze) and land-sea temperature contrasts
Latent heat is central to storm development and the energy budget of the atmosphere
Radiation processes and atmospheric absorption/emission underpin the greenhouse effect and climate forcing
The atmosphere is not a perfect blackbody; selective absorption shapes the infrared sky, the greenhouse effect, and the planetary energy balance