Heat transfer by radiation Knowledge-Based Study

Study notes

1. What is Thermal Radiation?

   Thermal radiation is the transfer of internal thermal energy between bodies by means of electromagnetic waves. Unlike conduction and convection, which require a physical material medium (solids, liquids, or gases) to transfer energy, radiation can travel across a complete vacuum.

   Key Properties of Radiation

   • Speed: Radiative energy propagates through a vacuum at the speed of light, $c \approx 3 \times 10^8\text{ m/s}$.
   • Ubiquity: Every substance with an absolute temperature above absolute zero ($T > 0\text{ K}$) continuously emits thermal radiation due to the microscopic thermal motions of its charged particles.
   • Spectral Nature: Thermal radiation spans a broad continuous spectrum of wavelengths, predominantly in the infrared (IR) region for everyday objects, extending into the visible and ultraviolet ranges at much higher temperatures.

   How Surfaces Affect Radiation

   The rate at which an object radiates and absorbs thermal energy depends critically on its surface properties, its surface area, and its absolute temperature.

   Emission and Absorption of Radiation

   • Dark, Matte Surfaces: Excellent absorbers and excellent emitters of thermal radiation. They reflect very little incident radiation.
   • Light, Shiny Surfaces: Poor absorbers and poor emitters of thermal radiation. They act as effective reflectors of incident electromagnetic waves.

   An ideal physical object that absorbs all incident electromagnetic radiation regardless of frequency or angle of incidence is termed a blackbody. A blackbody is also an ideal emitter (having an emissivity $\varepsilon = 1$). Real objects have an emissivity value satisfying $0 < \varepsilon < 1$.

   The Stefan-Boltzmann Law

   The total thermal power $P$ radiated by a surface of area $A$ and emissivity $\varepsilon$ at thermodynamic temperature $T$ is given by the Stefan-Boltzmann law:

   $$P = \varepsilon \sigma A T^4$$

   where $\sigma \approx 5.67 \times 10^{-8}\text{ W/(m}^2\cdot\text{K}^4)$ is the Stefan-Boltzmann constant.

   Net Rate of Heat Transfer

   When an object at temperature $T$ is placed in an enclosure or environment at temperature $T_{\text{env}}$, it emits radiation into the surroundings while simultaneously absorbing radiation from them. The net rate of heat transfer by radiation, $P_{\text{net}}$, is expressed as:

   $$P_{\text{net}} = \varepsilon \sigma A (T^4 - T_{\text{env}}^4)$$

   If $T > T_{\text{env}}$, $P_{\text{net}} > 0$ and the object experiences a net loss of thermal energy. When $T = T_{\text{env}}$, the object reaches thermal equilibrium, emitting and absorbing energy at identical rates.

   Clarifying Common Misconceptions

   • Misconception: "Only very hot objects emit radiation."
     Correction: All objects above $0\text{ K}$ emit thermal radiation, including ice cubes, room-temperature furniture, and the human body.
   • Misconception: "Radiation needs air to travel from one place to another."
     Correction: Electromagnetic radiation travels most efficiently through empty space. Solar energy reaching Earth across the vacuum of space is a primary example of radiation.

   Real-World Applications

   Radiative heat transfer governs many engineering and environmental processes:

   • Vacuum Flasks (Dewar Flasks): Utilize silvered interior walls to minimize heat transfer by radiation through reflection.
   • Spacecraft Thermal Control: Since space is a vacuum, radiation is the only mechanism available for dissipating excess heat generated by onboard systems.
   • Solar Collectors: Use blackened surfaces to maximize the absorption of radiant energy from the Sun.