Contents
The study of Physics Topics can help us understand and solve real-world problems, from climate change to medical imaging technology.
What Does Radiation Emitted By a Body Depend On? What are the Applications of Kirchhoff’s Law in Daily Life?
When radiation is incident on a surface, it is, in general, divided into three parts:
i) Reflection from the surface: A part of the incident radiation is reflected. The reflective power or reflectance (r) is defined as,
r \(=\frac{\text { amount of reflected radiation }}{\text { amount of incident radiation }}\)
Normally, r ≤ 1. The value r = 1 refers to a perfectly white surface, commonly called a perfectly white body.
ii) Transmission across the surface: A part of the incident radiation is transmitted across the surface. The transmittive power or transmittance (t) is defined as,
t \(=\frac{\text { amount of transmitted radiation }}{\text { amount of incident radiation }}\).
Here also, t ≤ 1. For t = 1, the material of the surface is called a perfectly transparent medium, or a diather-manous substance. On the other hand, t = 0 corresponds to a perfectly opaque, or athermanous substance.
iii) Absorption by the surface: A part of the incident radiation is absorbed by the surface. The absorptive power (a) of a surface is defined as,
a \(=\frac{\text { amount of radiation absorbed }}{\text { amount of incident radiation }}\)
Here again, a ≤ 1. A surface with a = 1 is called a perfectly black surface, or simply a perfectly black body. The value of a for lamp black and platinum-black are 0.96 and 0.98, respectively.
All of the three quantities r, t and a are ratios of two similar quantities (amounts of radiation). So, each of them is dimensionless and has no unit.
In fact, all of the three quantities r, t and a depend on the wavelength (λ) of radiation. So, rλ, tλ and aλ denote the reflective power, transmittive power and absorptive power of a surface at a certain temperature T and for a certain wavelength A. For example,
i) A blue surface is a good reflector of blue radiation, a negligible part being transmitted or absorbed. So for blue radiation incident of such a surface, r is high, but t or a is low.
ii) Glass is almost transparent for radiations of short wave-lengths (temperature of source ~ 1200°C), like X-rays or visible light; So, t ≈ 1. But for longer wavelengths (temperature of source ~ 100°C), relevant to thermal radiations, glass behaves as an almost opaque or ather-manous medium, so that t ≈ 0. This principle is utilised in greenhouses.
The temperature of a body increases due to radiation only when some part of the incident radiation is absorbed by its surface. Therefore, the absorptive power a turns out to be a very important property in case of thermal radiations.
Emission of Radiation
The rate of emission of radiation from a unit surface area of a body depends only on two properties of the body:
i) Nature of the surface: The rate of emission depends on the colour of the surface, on whether the surface is rough or shiny, and on whether is it smooth or porous, etc. This dependence is described by Kirchhoff’s law.
ii) Temperature of the body: Higher the temperature of a body, more is the rate of emission. The rate falls to zero only when a body is at the temperature of absolute zero, i.e., at T = 0. This dependence is described by Stefan’s law.
Emissive power (e): The amount of radiation emitted from a unit surface area of a body in unit time is called the emissive power of that particular surface kept at a particular temperature.
In general, this emissive power is different for different colours of radiation, i.e., for different wavelengths (λ).
If eλ denotes the emissive power of a surface for a wavelength λ, then the amount of radiation emitted per unit area of the surface per second between the wavelengths λ and λ + dλ will be eλdλ.
Total emissive power of the surface for all possible wavelengths is,
e = \(\int_0^{\infty} e_\lambda d \lambda\)
The units of emissive power are cal ᐧ cm-2 ᐧ s-1 in CGS system and J ᐧ M-2 ᐧ s-1 in SI.
1 J ᐧ m-2 ᐧ s-1 = \(\frac{1 \mathrm{~J}}{1 \mathrm{~m}^2 \times 1 \mathrm{~s}}\) = \(\frac{\frac{1}{4.2} \mathrm{cal}}{10^4 \mathrm{~cm}^2 \times 1 \mathrm{~s}}\)
= \(\frac{1}{42000}\) cal ᐧ cm-2 ᐧ s-1
A perfectly black surface is the best emitter of radiation at a particular temperature. In this context, the emission from any surface is sometimes compared with that from a perfectly black surface. A new quantity called relative emittance or emissivity or coefficient of emission (e) of a surface is then defined as,
Being a ratio between two amounts of heat, ε is dimensionless and has no unit. Of course, ε ≤ 1, the equality sign standing for a perfectly black surface.
Black body: A body that absorbs radiations of all wavelengths falling on it, without reflecting or transmitting any of it, is called an ideal black body. As it is an ideal absorber it is an ideal emitter as well. At a particular temperature, energy radiated by a black body is greater than that radiated by any other substance. Hence, radiation emitted by an ideal black body is called total radiation or black body radiation. In reality there is no ideal black body, though lamp black and platinum black is considered to be nearly ideal. Lamp black absorbs about 96% and platinum black absorbs about 98% of the radiation falling on them.
Ferry’S black body: A hollow double-walled metal sphere kept at a steady temperature with a fine hole behaves like an ideal black body. It is blackened inside with lamp black and nickel-polished on the outside [Fig.]. The space between the two walls do not have any air. So heat is not lost due to conduction and convection.
Heat radiation entering the sphere through the small opening O gets completely absorbed inside the sphere after a few successive reflections. The projection P, opposite to the opening O prevents normal reflection of the radiation. So no radiation entering the sphere through the opening can come out of the sphere. This means that the total radiation gets absorbed. Therefore the sphere acts as an ideal black body. This is known as Ferry’s blackbody.
Thermal radiation comes out of the opening when the body is heated. In fact the opening O acts as a black body and the intensity and nature of radiation depends only on the temperature of the body. Hence, this radiation is also called temperature radiation.
In fact, any hollow enclosure with a small opening acts as a nearly ideal black body. Radiant heat entering it has a negligible chance of coming out through the small opening. Good absorbers are good emitters; so these hollow enclosures emit intense black body radiations at high temperatures. In a coal furnace, the narrow gaps between the burning pieces of coal appear to be brighter than any piece of burning coal itself.
Kirchhoff’s Law
The relation between emissive power and absorptive power of a substance is expressed by Kirchhoff’s law. It states that the ratio between the emissive power and the absorptive power of any substance at a fixed temperature is equal to the emissive power of an ideal black body at that temperature which is constant.
Let at a fixed temperature T, the emissive power of a substance be e, its absorptive power be a and the emissive power of an ideal black body at that temperature be E. Then, by Kirchhoff’s law,
\(\frac{e}{a}\) = E …… (1)
Conclusions drawn from Kirchhoff’s law:
- The value of the ratio \(\frac{e}{a}\) increases with the increase in a temperature as E increases with the rise in temperature for a fixed wavelength.
- When T is kept constant, E is also a constant for a par-ticular wavelength of radiation. This means, if e is large, a is also large. So a good emitter is also a good absorber and vice versa for the same wavelength.
- Relative emittance or coefficient of emission, ε = \(\frac{e}{E}\); from Kirchhoff’s law, ε is equal to a, the absorptive power.
Applications:
i) A white china bowl is partially smeared with lamp black. Now, the bowl is heated to 1000°C. If we take this bowl to a dark room then the black coloured parts appear brighter than the rest. The black part is a better absorber than the white part. So, from Kirchhoff’s law, it is a good emitter as well. Thus, it appears brighter as it emits more heat.
ii) In a solar spectrum we see many black lines. These are called Fraunhofer lines. The origin of these lines can be explained with the help of Kirchhoff’s law. [This has been discussed in details in the chapter ‘Dispersion and Scattering of Light’ in Chhaya Physics XII.]
Examples of Emission and Absorption of Heat
I) Cups and saucers, mugs etc. which are used to serve hot beverages like tea and coffee are usually white and shiny. This helps to keep the beverage hot for a long period of time as heat loss due to radiation is very small.
ii) Dark or black coloured wet clothes dry up faster in sun than white wet clothes do. This happens because black clothes absorb the heat from the sun at a higher rate.
iii) It is comfortable to wear dark clothes in winter and white clothes in summer. Dark clothes keep our bodies warm by absorbing more heat emitted by the sun. During the summer, the white clothes absorb a very small fraction of the heat and reflect most of it. So our bodies remain cool.
iv) The cloth of an umbrella is usually made black. Being a good absorber, it collects the sun rays and also radiates out the heat fast. The radiated heat does not heat up the air below the umbrella and hence keeps the body cool.
v) Let us take two thermometers and blacken the bulb of one of them. If we keep these thermometers in the sun, after a while the temperature of the blackened thermometer will read more than the other one. This happens because the blackened bulb absorbs more heat from the sun.
vi) Humid air is a better absorber of heat than dry air. On a cloudy and humid day air absorbs more heat from the sun and becomes warmer. During night, the surface of the earth cools by radiating heat. But humid air is ather-manous to heat and it prevents the passage of heat to the outer space. Thus, humid and cloudy days and nights are warmer than clear ones.
vii) It is difficult to stay in houses with tin roofs during summer afternoon because tin absorbs heat. But at night, tin radiates the heat rapidly and cools. So the room becomes cold.
viii) Outer surface of a spacecraft is made smooth and shiny to reflect off radiated heat from the sun so that the spacecraft cannot get much heated.
ix) In coal ovens, spaces between the glowing pieces of coal appear brighter than the glowing coal pieces themselves. Any hole behaves like an ideal black body [Fig.], Hence, absorptive power as well as emissive power of the spaces is very high. So the spaces appear brighter.
x) Bottom surface of a cooking container is made black and rough so as to absorb more heat. Hence food is cooked faster in these containers than those with white and polished bottom.
xi) Highly polished shoes are more comfortable to wear since they reflect most of the incident heat and absorbs very little of it.
xii) In deserts, days are unbearably hot and nights are cold. Air in those regions being very dry, is diathermanous. During daytime, this dry air allows heat to easily pass through the atmosphere and heat the surface. At night, the earth’s surface radiates heat which easily escapes the atmosphere leaving the surface and the air around it cold. This is why extreme temperature changes are observed in deserts.
Greenhouse: In cold countries glass-houses and sometimes garden-houses with glass roofs are constructed. These are used to preserve plants and vegetables from withering away due to the low temperatures and so are called greenhouses. Glass is diathermanous to short waves.
Sun rays, because of its high temperature, are rich in shorter waves and can enter through the roof. Materials in the shade absorb the radiation and warm up. The radiations from these preserved materials mostly consist of long waves like heat waves as they are at quite low temperatures. Glass being athermanous to long waves, does not allow the radiation to escape and the interior of the house remains warm throughout the year.
Greenhouse effect: Due to the presence of certain gasses in earth’s atmosphere, the earth acts as a huge greenhouse. These gases are present in trace amounts and are known as greenhouse gases. Water-vapour, carbon dioxide, methane, nitrous oxide, chloroflurocarbons etc. are some important greenhouse gases. These gases form a layer in the atmosphere which is diathermanous to short heat waves, but athermanous to long waves. So, the sun rays, being of short wavelength can enter the earth’s atmosphere.
However, the heat radiated from the earth’s surface is of longer wavelength and cannot pass through the gaseous layer. This warms up the air and the earth’s surface. This is called greenhouse effect. In absence of this effect the average temperature of the earth’s surface would have been lower by 30 °C-35 °C approximately. The atmosphere would then be adverse for life.
Enhanced greenhouse effect: Due to human activities, the amount of the greenhouse gases in air is increasing alarmingly. This results in the increase in air and earth’s temperature regularly. This is called enhanced greenhouse effect.
If this enhanced greenhouse effect is not controlled, immediately the existence of life on earth will be in danger in the future.
Harmful effects of global warming:
- There will be acute shortage of water for consumption and for use in agri-cultural and electricity production. There will also be degradation in the quality of drinking water.
- Due to melting of ice on mountains and polar regions sea level will rise causing large areas on the earth’s surface to submerse under water.
- Death rate of plants and animals will increase.
- Forest resources will show signs of destruction.