A wave of radiation falls on a body, 35% of the radiation is reflected back. If transmissivity of the body is 0.25, then emissivity is:
0.40
Understanding Radiation Interaction and Emissivity
When radiation encounters a surface, it can be reflected, absorbed, or transmitted. The way a surface interacts with radiation is described by its reflectivity ($\rho$), absorptivity ($\alpha$), and transmissivity ($\tau$). These properties are related by a fundamental conservation principle.
Radiation Interaction Principles
For any material interacting with incident radiation, the sum of the fractions that are reflected, absorbed, and transmitted must equal the total incident radiation. This can be expressed as:
$$ \rho + \alpha + \tau = 1 $$- Reflectivity ($\rho$): The fraction of incident radiation that is reflected by the surface.
- Absorptivity ($\alpha$): The fraction of incident radiation that is absorbed by the surface.
- Transmissivity ($\tau$): The fraction of incident radiation that passes through the surface.
Calculating Absorptivity
In this problem, we are given:
- Reflectivity, $\rho = 35\% = 0.35$
- Transmissivity, $\tau = 0.25$
We can use the conservation principle to find the absorptivity ($\alpha$):
$$ \alpha = 1 - \rho - \tau $$ $$ \alpha = 1 - 0.35 - 0.25 $$ $$ \alpha = 1 - 0.60 $$ $$ \alpha = 0.40 $$So, the absorptivity of the body is 0.40.
Relating Absorptivity to Emissivity
Kirchhoff's Law of thermal radiation is crucial here. It states that for a body in thermal equilibrium with its surroundings, the emissivity ($\epsilon$) of the body at a specific wavelength and temperature is equal to its absorptivity ($\alpha$) at the same wavelength and temperature.
Therefore, according to Kirchhoff's Law:
$$ \epsilon = \alpha $$Determining Emissivity
Since we calculated the absorptivity ($\alpha$) to be 0.40, the emissivity ($\epsilon$) of the body is also 0.40.
$$ \epsilon = 0.40 $$This means the body emits radiation effectively at a level equivalent to its ability to absorb radiation under the same conditions.
Important Questions from Radiation
A body whose absorptivity does not vary with temperature and wavelength of the incident ray is known as
The heat of the sun reaches us according to
Heat is transferred from an electric bulb by ______.
A room window (consisting of a vertical sheet of plane glass) is exposed to direct sunshine at a strength of 1000 W/m2. The window is pointing due south, while the sun is in the southwest, 30° above the horizon. Estimate the amount of solar energy in W/m2 reflected by the window. Assume glass to be gray with ρ(reflectivity) = 0.08.
- Radiosity is defined as _______.
