NEET Physics Notes Mechanics-Transfer of heat-Perfectly Black Body
Perfectly Black Body
A perfectly black body is the one which completely absorbs the radiations of all the wavelengths that are incident on it. Thus, absorbing power of a perfectly black body is 1 (i.e a = 1).
No material body is a perfectly black body. However, lamp black and platinum black are nearly perfectly black bodies. For scientific work, we prepare black bodies by special techniques. Fery’s black body and Wien’s black body are commonly used in laboratories.
For perfectly black body, a = 1, r = t = 0
For a perfect reflector, a=t = 0, r = 1
For a perfect transmitter, a = r = 0,t = 1
Emissive Power and Emissivity
Total emissive power of a given surface at a given temperature is defined as the total amount of radiant energy emitted per unit surface area per unit time by the body. SI unit of emissive power is WnT2.Emissive power of a surface depends on the nature of the surface and its temperature. Emissivity of a body at a given temperature is defined as the ratio of the total emissive power of the black body (e) to the total emissive power of perfectly black body (E) at that temperature
A perfectly black body is also the perfect emitter i.e. it emits radiations of all possible wavelengths at that temperature.
Kirchhoff’s Law of Radiation
Kirchhoff s law of radiation states that the ratio of emissive power to absorptive power of a body, is same for all surfaces at the same temperature and is equal to the emissive power of a perfectly black body at that temperature. Mathematically,
Kirchhoffs law implies that a good absorber is a good emitter (or radiator) to.
Fraunhoffer’s lines (dark lines observed in solar spectrum) can be easily explained on the basis of Kirchhoffs laws.
Stefan’s Law
According to the Stefan’s law, the emissive power of a perfectly black body (energy emitted by black body per unit surface area per unit time) is directly proportional to the fourth power of its absolute temperature.
The radiant power {P), i.e. energy radiated by a body per unit time is given by
If a body at temperature T is surrounded by another body at temperature T0 (where, T0 < T), then Stefan’s law is modified as,
Newton’s Law of Cooling
According to the Newton’s law of cooling, rate of cooling of a body is directly proportional to the temperature difference between the body and the surroundings, provided the temperature difference is small.Mathematically,
where, k is a constant.
Newton’s law of cooling is a special case of Stefan’s law under the condition that the temperature difference is small enough.
If a body cools by radiation through a small temperature difference from T1 to T2 in a short time t when the surrounding temperature is T0, then
Black Body Spectrum
The black body spectrum is a continuous spectrum as shown in the figure. At a given temperature, initially the intensity of thermal radiation increases with an increase in wavelength and reaches a maximum value at a particular wavelength λm. On increasing the wavelength beyond λm, the intensity of radiation Eλ starts decreasing.
Variation of intensity of thermal radiation with wavelength is shown below.
The total area under Eλ – λ curve gives the total intensity of radiation at that temperature. The area, in accordance with the Stefan’s law of radiation, is directly proportional to the fourth power of the temperature.
Wien’s Displacement Law
From Eλ – λ graph, we find that as the temperature T of a black body increases, the wavelength λm corresponding to the maximum emission decreases such that 
or λmT= constant = b, where b is known as the Wien’s constant and its value is 2.89 x 10-3 mK.
Solar Constant
The amount of heat redeived from the sun by one square centimeter area of a surface placed normally to the sun rays at mean distance of the earth from the sun is known as solar constant. It is denoted by S
where, r is the radius of sun and R is the mean earth’s distance from sun value of solar constant S = 1937 cal/cm2/min.