Absorption, Reflection and Transmission of Heat Radiation

Radiation as a mode of heat transfer

Heat can be transferred by conduction, convection and radiation. The first two require a material medium; radiation does not. The term radiation refers both to this mode of heat transfer and to the continuous emission of energy from the surface of any body because of its thermal energy. That emitted energy is called radiant energy and is in the form of electromagnetic waves, so radiation is the fastest mode of transfer of heat and can take place through vacuum as well as through a material medium transparent to the radiation. Physical contact between the bodies exchanging heat is not required. The commonest example is the transfer of heat and light from the Sun to the Earth.

Electromagnetic radiation emitted by bodies at a temperature higher than that of their surroundings is called thermal radiation. When it falls on a body that is not transparent to it, it is absorbed and the body gets heated up.

Interaction of thermal radiation and matter

Whenever thermal radiation falls on the surface of an object, some part of the heat energy is reflected, some part is absorbed and the remaining part is transmitted. Let $Q$ be the total thermal energy incident on the surface and $Q_{a}$, $Q_{r}$, $Q_{t}$ the amounts absorbed, reflected and transmitted. Then

$$Q = Q_{a} + Q_{r} + Q_{t}$$

Dividing throughout by $Q$,

$$1 = \dfrac{Q_{a}}{Q} + \dfrac{Q_{r}}{Q} + \dfrac{Q_{t}}{Q}$$

$$\therefore \ a + r + t_{r} = 1$$

Definitions

• Coefficient of absorption (absorptive power, absorptivity) $a$: the ratio of the amount of heat absorbed to the total quantity of heat incident, $a = \dfrac{Q_{a}}{Q}$.

• Coefficient of reflection (reflectance) $r$: the ratio of the amount of radiant energy reflected to the total energy incident, $r = \dfrac{Q_{r}}{Q}$.

• Coefficient of transmission (transmittance) $t_{r}$: the ratio of the amount of radiant energy transmitted to the total energy incident, $t_{r} = \dfrac{Q_{t}}{Q}$.

Since all three are ratios of thermal energies, they are dimensionless quantities and have no units.

Special cases

• If $r = 0$ and $a = 0$, then $t_{r} = 1$: all the incident energy is transmitted, and the object is a perfect transmitter, said to be completely transparent to the radiation.

• If $t_{r} = 0$ and $a + r = 1$, the object does not transmit any radiation and is said to be opaque to it.

• If $t_{r} = 0$ and $a = 0$, then $r = 1$: all the incident energy is reflected, and the object is a perfect reflector. A good reflector is a poor absorber and a poor transmitter.

• If $r = 0$ and $t_{r} = 0$, then $a = 1$: all the incident energy is absorbed, and the object is a perfect blackbody.

Diathermanous and athermanous substances

A substance through which heat radiations can pass is a diathermanous substance; for such a body $t_{r} \neq 0$. A diathermanous body is neither a good absorber nor a good reflector. Substances which are largely opaque to thermal radiation, that is, which do not transmit the heat radiation incident on them, are athermanous substances.

Dependence on wavelength

The values of $a$, $r$ and $t_{r}$ depend not only on the material of the object but also on the wavelength of the incident radiation. Hence the same object may be athermanous or diathermanous for certain wavelengths and a good absorber for certain other wavelengths. This is why a car left in sunlight with its windows closed becomes warmer inside than the outside air: the glass is diathermanous to the short-wavelength radiation from the Sun, which enters and is absorbed inside, but athermanous to the long-wavelength infrared radiation re-emitted by the warm interior, which is therefore trapped.

Standard results

$$Q = Q_{a} + Q_{r} + Q_{t}, \qquad a + r + t_{r} = 1$$

$$a = \dfrac{Q_{a}}{Q}, \qquad r = \dfrac{Q_{r}}{Q}, \qquad t_{r} = \dfrac{Q_{t}}{Q}$$

• $a$, $r$, $t_{r}$ are dimensionless; $a = 1$ for a perfect blackbody, $r = 1$ for a perfect reflector, $t_{r} = 1$ for a perfect transmitter.