### Perfectly Black Body

• Define radiation mode of heat transfer.

• Define absorptivity, reflectivity, transmissivity, black Body, grey body, opaque body.

• Relations between emissivity and absorptivity.

A body which absorbs all incident light is referred to ’Perfectly black body’. A black body would not reflect and would not transmit any light falling on it.
In practice, a hollow enclosure having a small hole is the nearest approach to a black body because the radiation entering the chamber through the hole is absorbed completely due to repeated reflections inside the enclosure. Radiation emerging from the small hole of such a hollow enclosure is negligible.
Black body radiation: Radiation from a black surface depends only on temperature and does not depend on the nature of the surface. At lower temperature radiations are small. With increasing temperature amount of radiations increase but the quantity of radiations with small energy is decreased.

## Types of Bodies:

• General Body
For general body,

$\alpha + \rho + \tau = 1$

where
$\alpha$ = absorptivity (ratio of energy absorbed to incident energy)
$\rho$ = reflectivity (ratio of energy reflected to incident energy)
$\tau$ = transmissivity (ratio of energy transmitted to incident energy)

• Opaque Body
For an opaque body: $\alpha$ + $\rho$ = 1

• Gray Body:
A gray body is one for which, $\alpha = \epsilon, (0 < \alpha < 1; 0 < \epsilon < 1),$ where $\epsilon$ = the emissivity of the body For a gray body:

$\epsilon + \rho = 1$

Real bodies are frequently approximated as gray bodies.
A diffused surface is a surface from which directions of emitted, reflected and incident radiations are unknown or is unpredictable.

### Solved Example:

#### 82-1-01

All radiations in a perfectly black body are:

### Solved Example:

#### 82-1-02

The amount of radiation mainly depends on:

### Solved Example:

#### 82-1-03

A perfect black body is one which:

### Solved Example:

#### 82-1-04

A grey body is one whose absorptivity: (ISRO RAC 2014)

### Solved Example:

#### 82-1-05

Depending on the radiating properties, a body will be considered perfectly black when:

Solution:
$\alpha$ = absorptivity, $\rho$ = reflectivity, $\tau$ = transmissivity.

### Solved Example:

#### 82-1-06

Coefficient of transmission and coefficient of reflection for a given body are 0.22 and 0.74 respectively. Then, at a given temperature, the coefficient of emission for the body is:

Solution:
Reflectivity ($\rho$) + Absorptivity ($\alpha$) + Transmissivity ($\tau$)= 1

### Solved Example:

#### 82-1-07

The coefficient of absorption of a perfectly black body is: