Radiation

Radiation is the mode of heat transfer that does not require any material medium for propagation. Unlike conduction and convection, which rely on the thermal vibration of atoms or the bulk movement of fluids, radiation occurs through electromagnetic waves. It propagates at the speed of light (c ≈ 3 × 10⁸ m/s) in a vacuum and obeys the laws of optics, such as reflection, refraction, and total internal reflection.

Fundamental Properties of Thermal Radiation

Thermal radiation consists of electromagnetic waves emitted by a body solely due to its temperature. Every object at a temperature above absolute zero (0 K or -273.15°C) continuously emits thermal radiation.

• Electromagnetic Spectrum Range: Thermal radiation primarily spans the infrared region, visible light spectrum, and a portion of the ultraviolet region (0.1 μm to 100 μm).
• Medium Independence: It can travel through a perfect vacuum. Solar energy reaches the Earth’s atmosphere entirely via radiation.
• Prevailing Interaction: When radiation falls on a body, it is partially absorbed, partially reflected, and partially transmitted.

The Radiation Equation

For any surface where radiation is incident, the total energy is conserved based on the coefficients of absorption, reflection, and transmission:

Where:

• a = Absorptivity (fraction of incident radiation absorbed)
• r = Reflectivity (fraction of incident radiation reflected)
• t = Transmissivity (fraction of incident radiation transmitted)

Idealized Classifications of Bodies

Body Type	Mathematical Condition	Physical Characteristics	Real-world Example
Black Body	a = 1, r = 0, t = 0	Absorbs 100% of incident radiation; reflects or transmits none.	Lamp black, Platinum black, Ferry’s Blackbody.
Opaque Body	t = 0 ⇒ a + r = 1	Does not allow any radiation to pass through its structure.	Wood, thick metals, bricks.
White Body	r = 1, a = 0, t = 0	Reflects all incident radiation completely.	Polished silver mirror.
Diathermanous	t = 1, a = 0, r = 0	Perfectly allows thermal radiation to pass through without heating up.	Rock salt, pure dry air, Quartz.
Athermanous	t = 0	Completely prevents the transmission of thermal radiation.	Water vapor, carbon dioxide, glass.

Governing Laws of Blackbody Radiation

Prevost’s Theory of Heat Exchanges

This theory states that all bodies at all temperatures above absolute zero emit thermal radiation to their surroundings and simultaneously absorb radiation from them.

• Thermal Equilibrium: When the rate of emission equals the rate of absorption, the temperature of the body remains constant.
• Heating and Cooling: If emission exceeds absorption, the body cools down; if absorption exceeds emission, the body heats up. Emission does not stop at thermal equilibrium.

Stefan-Boltzmann Law

The total radiant energy (E) emitted per unit surface area per second by a perfectly black body is directly proportional to the fourth power of its absolute temperature (T).

For a non-black body with emissivity (ϵ): Where:

• σ = Stefan-Boltzmann constant ≈ 5.67 × 10^-8 W/m^2K4.
• ϵ = Emissivity of the surface (0 < ϵ < 1). For a perfect blackbody, ϵ = 1.
• T = Absolute temperature measured in Kelvin (K).

Kirchhoff’s Law of Thermal Radiation

At any given temperature, the ratio of the emissive power (E) to the absorptive power (a) is constant for all bodies and is equal to the emissive power of a perfectly black body (E_b) at that same temperature.

• UPSC Prelims Takeaway: Good absorbers are good emitters, and poor absorbers are poor emitters.

Wien’s Displacement Law

The wavelength (λ_m) corresponding to the maximum intensity of radiation emitted by a black body is inversely proportional to its absolute temperature (T).

Where:

• b = Wien’s displacement constant ≈ 2.898 × 10^-3 m·K.
• Application: As an object gets hotter, its peak emitted wavelength shifts toward shorter wavelengths (from infrared to red, then orange, yellow, and eventually blue/white).

Newton’s Law of Cooling

The rate of loss of heat (-dQ/dt) of a body is directly proportional to the temperature difference between the body (θ) and its surroundings (θ₀), provided the temperature difference is small (typically less than 30°C).

• Limitation: This is a simplified, linear approximation derived from the Stefan-Boltzmann law under low-temperature differentials.

Everyday Phenomena and Applications of Radiation

Greenhouse Effect and Atmospheric Dynamics

The greenhouse effect is driven by the selective transmission properties of atmospheric gases. Solar radiation (short wavelength, high frequency) easily penetrates the Earth’s atmosphere and heats the planetary surface. The Earth then re-radiates this energy as terrestrial radiation (long-wavelength infrared). Greenhouse gases (GHGs) like CO₂, CH₄, and water vapor are athermanous to long waves; they absorb this terrestrial radiation and re-emit it, trapping heat within the troposphere.

Solar Constant and Solar Radiation

The solar constant (S) is the amount of solar radiant energy received per second per unit area held normal to the direction of solar rays at the mean distance of the Earth from the Sun. Its standard value is approximately 1.361 kW/m² (or ≈ 1361 W/m²).

Additional Application Metrics

• Thermos Flask (Dewar Flask): Minimizes radiation losses by silvering the inner walls. The silvered surface reflects radiating heat back into the liquid, while preventing external radiation from penetrating inside.
• Color-Based Absorption: White and light-colored clothes are preferred in summer because they possess high reflectivity (r → 1) and low absorptivity (a → 0). Dark clothes are worn in winter due to high absorptivity (a → 1).
• Astrophysical Temperature Measurement: The temperatures of stars, including the Sun, are calculated using Wien’s Displacement Law and Stefan’s Law based on the spectral analysis of light received by space observatories.

Last Modified: May 28, 2026