Question

Fig. 5.40 shows the plot of the function y (x) representing a fraction of the total power of thermal radiation falling within the spectral interval from 0 to x. Here x = λ/λm (λm is the wavelength corresponding to the maximum of spectral radiation density). Using this plot, find:

(a) the wavelength which divides the radiation spectrum into two equal (in terms of energy) parts at the temperature 3700 K;

(b) the fraction of the total radiation power falling within the visible range of the spectrum (0.40-0.76 μm) at the temperature 5000 K;

(c) how many times the power radiated at wavelengths exceeding 0.76 μm will increase if the temperature rises from 3000 to 5000 K.

Answer 1

(a) From the curve of the function y(x) we see that y = 0.5 when x = 1.41

So the visible range (0.40 to 0.70) μm corresponds to a range (0.69 to 1.31) of x

From the curve

y (0.69 ) = 0.07

y( 1.31) = 0.44

so the fraction is 0.37

(c) The value of x corresponding to 0.76 are