Radiation

Radiation: The Third Mode of Heat Transfer

Heat can travel through empty space. That is the central fact that sets radiation apart from conduction and convection. While conduction requires direct contact between particles and convection needs a fluid medium to carry heat through bulk motion, radiation requires no medium at all. The Sun's energy reaches Earth across 150 million kilometres of vacuum — that alone proves radiation is a fundamentally different physical process.

All objects emit thermal radiation simply because they have a temperature above absolute zero. This radiation is electromagnetic in nature, spanning a continuous spectrum that shifts with temperature. At ordinary temperatures (say, a block of iron at 300 K), the emitted radiation lies entirely in the infrared region — invisible to the eye but detectable as warmth. Heat an object to about 800 K and it begins to glow dull red; at 3000 K (like a tungsten filament) it emits visible light along with copious infrared.

The Nature of Thermal Radiation

Thermal radiation is emitted by every body at every instant. The rate at which energy is radiated depends strongly on the body's temperature and on the nature of its surface. A black, rough surface is a much better emitter (and absorber) than a polished, white surface. This is why car radiators are painted black — they need to shed heat efficiently.

The radiation itself consists of electromagnetic waves of all wavelengths. The distribution of energy across these wavelengths follows a characteristic curve that peaks at a wavelength inversely proportional to temperature. This is why a piece of metal first glows red (longer wavelengths), then white (all visible wavelengths), as its temperature rises.

Properties of Thermal Radiation

The textbook lists four fundamental properties that govern how thermal radiation behaves. Each one is a direct consequence of the electromagnetic nature of the radiation and the laws of thermodynamics.

Property 1: All bodies emit thermal radiation at all temperatures above 0 K.

This is not a matter of "if" but "how much." Even a block of ice at 273 K emits infrared radiation — you can detect it with a thermal camera. The rate of emission increases rapidly with temperature, as we will see in the Stefan-Boltzmann law.

Property 2: The radiation emitted by a body is a continuous spectrum covering all wavelengths, from very long infrared to very short ultraviolet.

Unlike the discrete spectral lines emitted by excited atoms (which come from electronic transitions), thermal radiation is a continuous smear of wavelengths. The energy is distributed smoothly, with a single peak that shifts according to Wien's displacement law.

Property 3: The intensity of radiation (energy emitted per unit area per unit time) increases very rapidly with temperature.

This is not a linear relationship. Double the absolute temperature of a body and its radiated power increases by a factor of 16. This dramatic dependence is captured by the Stefan-Boltzmann law.

Property 4: Good absorbers of radiation are also good emitters, and good reflectors are poor emitters.

This is the principle of reciprocity. A black surface that absorbs nearly all incident radiation will, when heated, emit radiation very efficiently. A polished silver surface that reflects most radiation will emit very little. This is why a thermos flask has a silvered inner surface — it minimises both absorption of outside radiation and emission of heat from the contents.

The Stefan-Boltzmann Law

This is the central quantitative result for thermal radiation. It states that the total power radiated per unit area of a blackbody is proportional to the fourth power of its absolute temperature.

where:

• $P$ is the total power radiated (in watts)
• $A$ is the surface area of the body (in m²)
• $T$ is the absolute temperature (in K)
• $\sigma$ is the Stefan-Boltzmann constant, $\sigma = 5.67 \times 10^{-8} \ \text{W m}^{-2} \ \text{K}^{-4}$

For a body that is not a perfect blackbody, we introduce the emissivity $\epsilon$ (a number between 0 and 1):

The emissivity depends on the material and the surface finish. For a perfectly black surface, $\epsilon = 1$; for a perfectly reflecting surface, $\epsilon = 0$.

Wien's Displacement Law

As the temperature of a blackbody increases, the wavelength at which its emission is strongest shifts to shorter values. This is described by Wien's displacement law:

where $\lambda_m$ is the wavelength of maximum emission (in metres) and $T$ is the absolute temperature (in K).

This law explains several everyday observations:

• A piece of iron heated to about 800 K glows red ($\lambda_m \approx 3.6 \times 10^{-6}$ m, in the red part of the spectrum)
• The Sun's surface at about 5800 K has $\lambda_m \approx 5.0 \times 10^{-7}$ m, which is in the yellow-green — right in the middle of the visible spectrum
• A very hot star (say 30,000 K) peaks in the ultraviolet and appears blue-white

The Greenhouse Effect

The textbook uses the greenhouse effect as an important application of these principles. The mechanism works as follows:

1. Visible light from the Sun (short wavelengths, around $5 \times 10^{-7}$ m) passes through the glass of a greenhouse almost unhindered.
2. This radiation is absorbed by the soil, plants, and interior surfaces, heating them.
3. These warm objects re-emit thermal radiation, but at much longer wavelengths (infrared, around $10^{-5}$ m) because their temperature is far lower than the Sun's.
4. Glass is opaque to infrared radiation — it absorbs these long wavelengths and re-radiates some of the energy back into the greenhouse.
5. The net effect is that the interior of the greenhouse stays warmer than the outside air.

The same principle operates on a global scale with Earth's atmosphere. Carbon dioxide, methane, and water vapour act like the glass — they are transparent to incoming sunlight but absorb outgoing infrared radiation. This is the natural greenhouse effect that keeps Earth's average temperature about 33 K warmer than it would be without an atmosphere.

Radiation and Colour: Everyday Applications

The properties of thermal radiation discussed above — that black, rough surfaces absorb and emit radiant energy far more efficiently than light-coloured or shiny surfaces — have direct, familiar consequences.

This is why we choose to wear white or light-coloured clothes in summer: a light-coloured, shiny fabric reflects and absorbs a much smaller fraction of the incident solar radiation than a dark fabric would, so the body stays cooler. In winter, we tend to wear dark-coloured clothes for the opposite reason — a dark surface absorbs incident radiation (including sunlight and radiation from other warm surroundings) more efficiently, helping to keep the body warm.

The same principle explains why the bottoms of cooking vessels are blackened: a blackened surface absorbs radiant heat from the flame far more efficiently than a bright, polished one, so the pot heats up faster and cooks more efficiently.

The Dewar Flask (Thermos Bottle)

A Dewar flask, more familiarly known as a thermos bottle, is a practical device designed to keep a hot liquid hot or a cold liquid cold for as long as possible — that is, to minimise heat transfer by all three modes at once.

Its construction directly targets each mode:

• The flask has double walls, with the space between them evacuated (pumped to a near-vacuum). Since conduction and convection both require a material medium to carry heat, this vacuum gap virtually eliminates heat transfer by conduction and convection between the inner and outer walls.
• The two facing surfaces of the double wall are silvered (coated with a highly reflective, low-emissivity layer). Since a shiny silvered surface is a poor absorber and a poor emitter of thermal radiation, this greatly reduces heat transfer by radiation across the vacuum gap.
• The flask's contents are supported by a cork or plastic stopper and stand, both poor conductors of heat, which minimises the small remaining conduction path to the outside through the neck and base of the flask.