Problem 5.258

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 $x=\lambda / \lambda_{m}\left(\lambda_{m}\right.$ 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 $3700 \mathrm{~K}$; (b) the fraction of the total radiation power falling within the visible range of the spectrum $(0.40-0.76 \mu \mathrm{m})$ at the temperature $5000 \mathrm{~K}$ (c) how many times the power radiated at wavelengths exceeding $0.76 \mu \mathrm{m}$ will increase if the temperature rises from 3000 to $5000 \mathrm{~K}$