Question

Calculate the expected ∆Tb =
T^2_b/λ(2c) when c = 0.05.

Answer 1

The above equation presents the form of Wein's dispalcement law which states thatone of the relations between the emission spectrum of a black body and its temperature. It states that the higher the temperature, the lower the wavelength λmax for which the radiation curve reaches its maximum. The shift to shorter wavelengths corresponds to photons of higher energies. In other words, λmax (peak wavelength) is inversely proportional to temperature.

Accordingly

λmax= b / T

where:

λmax is the aforementioned peak wavelength of light,

T is an absolute temperature of a black body im kelvin

b = 2.8977729 mm*K is the Wien's displacement constant.

Puttting the values in the above equation

λmax= 10607 nm

If we consider the above equation and put the values for

∆Tb =T^2_b/λ(2c)

then T=273.05 K , b=2.8977729*10-3 m*K

∆Tb={(273.05)^(2*2.8977*10-3)2}/(10607*10^-9*2*3*10^8)

=11 mm