Physics · Thermal Properties Of Matter · NEET
E = sigma T^4 is the energy radiated per unit area per unit time (per square metre per second). To get the total power H you multiply by the surface area A and the emissivity e: H = A e sigma T^4. For a perfect black body e = 1. So E is a per-area quantity; H is the full power leaving the whole body.
Always use absolute temperature in kelvin. The law is E is proportional to T^4, and this only works for the absolute (Kelvin) scale where T starts at absolute zero. If a value is given in Celsius, convert first using T(K) = T(C) + 273. Using Celsius here gives completely wrong answers.
It means if you double the absolute temperature, the radiated energy does not double, it becomes 2^4 = 16 times larger. If T triples, energy becomes 3^4 = 81 times larger. A small rise in temperature causes a very large rise in radiation. This steep growth is the key idea NEET tests.
E = sigma T^4 is the ideal per-area emission of a perfect black body. H = A e sigma T^4 is the real total power for any body: A is surface area and e (emissivity, between 0 and 1) tells how close the body is to a perfect radiator. A tungsten lamp has e about 0.4, so it emits less than a perfect black body at the same temperature.
A body at temperature T with surroundings at temperature T0 both emits and absorbs radiation. The net power radiated is H(net) = A e sigma (T^4 - T0^4). If T > T0 the body loses heat; if T < T0 it gains heat. Use this whenever the question mentions a room or surrounding temperature.
A spherical black body of radius 12 cm radiates 450 W power at 500 K. If the radius were halved and the temperature doubled, the power radiated (in watt) would be:
The power radiated by a black body is P and it radiates maximum energy at wavelength lambda0. If the temperature is changed so that it now radiates maximum energy at wavelength (3/4) lambda0, the power radiated becomes nP. The value of n is:
Try the real previous-year questions from this chapter — each with the answer and a full solution.
It is the constant sigma in E = sigma T^4. Its SI value is 5.67 x 10^-8 W m^-2 K^-4. It was found experimentally by Stefan and later proved theoretically by Boltzmann.
The pure form E = sigma T^4 is for a perfect black body. Real bodies emit a fraction of this, so we use H = A e sigma T^4 where e is the emissivity, between 0 and 1.
It is W m^-2 K^-4 (watt per square metre per kelvin to the fourth power). This makes E come out in W m^-2 when T is in kelvin.
Wien's law gives temperature from the peak wavelength (lambda(max) is proportional to 1/T). Once you find the temperature ratio from Wien's law, you feed it into Stefan's law (P is proportional to T^4) to get the power ratio. Many NEET questions chain the two.
Because the power depends on the fourth power of temperature. A ratio like 1.1 becomes 1.1^4 which is about 1.46, so even a 10 percent temperature rise raises radiated power by about 46 percent.
