**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 T_{0} (where, T_{0} < 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 T_{1} to T_{2} in a short time t when the surrounding temperature is T_{0}, 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 λ_{m}. On increasing the wavelength beyond λ_{m}, the intensity of radiation E_{λ} starts decreasing.

Variation of intensity of thermal radiation with wavelength is shown below.

The total area under E_{λ }– 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 E_{λ }– λ graph, we find that as the temperature T of a black body increases, the wavelength λ_{m} corresponding to the maximum emission decreases such that

or λ_{m}T= 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/cm^{2}/min.