Question

How does radiosity for a surface differ from the emitted energy? For what kind of surfaces are these two quantities identical?

Short answer

Answer: Radiosity is the total amount of energy leaving a surface per unit area and time, including both emitted and reflected energy. Emitted energy is the amount of energy generated and released by a surface per unit area and time, depending on the surface's emissivity and temperature. Radiosity and emitted energy are identical for surfaces with ideal black-body characteristics, which have an emissivity of 1 and absorb all incident energy, converting it into emitted energy with no reflected energy.

Step-by-step solution

1. Definition of Radiosity

Radiosity (B) is the total amount of energy leaving a surface per unit area and time. It is the sum of both emitted energy and reflected energy. It takes into account all the energy interactions between the given surface and other objects in the scene.

2. Definition of Emitted Energy

Emitted energy (E) is the amount of energy generated and released by a surface per unit area and time. It depends on the surface's emissivity and temperature. It is important to note that not all surfaces emit energy; only those with non-zero emissivity emit energy.

3. Relationship between Radiosity and Emitted Energy

Radiosity and emitted energy are related for a given surface as: B = E + R, where R is the reflected energy (energy arriving at the surface from other surfaces and reflected back).

4. Identical Scenarios for Radiosity and Emitted Energy

Radiosity and emitted energy are identical for surfaces with ideal black-body characteristics. These surfaces have an emissivity of 1, meaning they absorb all the incident energy and convert it into emitted energy. In this case, there is no reflected energy (R = 0), so B = E.

Key concepts

Emitted Energy

Emitted energy refers to the energy released by a surface due to its own thermal state. Imagine it as the inherent power a surface has to radiate heat.
This energy is based on two key factors:

• Emissivity: A measure of how efficiently a surface emits energy. Surfaces with high emissivity release more energy.
• Temperature: The hotter the surface, the more energy it emits. This is governed by the Stefan-Boltzmann law, which states that the energy emitted by a surface is proportional to the fourth power of its temperature.

Only surfaces with a non-zero emissivity emit energy. This means that a perfect emitter, also known as a black body, would have an emissivity equal to 1, making it an ideal radiator of energy. In practical situations, however, most surfaces have emissivities less than 1, so they emit less energy than a perfect black body.

Reflected Energy

When energy strikes a surface, not all of it is absorbed. Some of it is bounced back into the environment. This bounced energy is known as reflected energy.
Reflected energy is an integral part of understanding overall energy interactions in environments. Surfaces with lower emissivity often reflect more energy because they do not absorb as much.
Understanding reflections is crucial for fields like architectural design, where controlling light and heat is essential. Surfaces with different textures and materials can reflect varying amounts of energy, influencing indoor lighting and temperature.
The sum of the emitted and reflected energy from a surface contributes to its radiosity, which is the total outflow of energy from the surface.

Black-Body Characteristics

A black body is an idealized surface that absorbs all incident radiation, regardless of frequency or angle. This makes it a perfect emitter, as it will eventually radiate this energy as emitted energy.
Key characteristics of a black body include:

• Emissivity Equal to 1: This means it neither reflects nor transmits any energy. All energy hitting the surface is absorbed and re-emitted.
• Perfect Radiator: It can emit the maximum possible energy for its temperature, according to the Stefan-Boltzmann law.

In scenarios where a surface behaves as an ideal black body, the radiosity equals the emitted energy. This occurs because no energy is reflected (reflected energy = 0), allowing us to focus purely on the emission.
While true black bodies don't exist in reality, many surfaces try to approximate these characteristics to improve energy efficiency in applications like heaters and photovoltaic devices.