Question 12.2: The spectral distribution of surface irradiation is as follo...

Known: Spectral distribution of surface irradiation.

Find: Total irradiation.

Analysis: The total irradiation may be obtained from Equation 12.19.

G = \int_{0}^{∞}{G_{λ}(λ)  dλ}            (12.19)

G = \int_{0}^{∞}{G_{λ}  dλ}

The integral is readily evaluated by breaking it into parts. That is,

G = \int_{0}^{5  μm}{G_{λ}  dλ} + \int_{5  μm}^{20  μm}{G_{λ}  dλ} + \int_{20  μm}^{25  μm}{G_{λ}  dλ} + \int_{25  μm}^{∞}{G_{λ}  dλ}

Hence

G = \frac{1}{2}(1000  W/m^{2} · μm)(5  –  0)  μm + (1000  W/m^{2} · μm)(20  –  5)  μm + \frac{1}{2}(1000  W/m^{2} · μm)(25  –  20)  μm + 0\\ = (2500 + 15,000 + 2500)  W/m^{2}\\ G = 20,000  W/m^{2}

Comments: Generally, radiation sources do not provide such a regular spectral distribution for the irradiation. However, the procedure of computing the total irradiation from knowledge of the spectral distribution remains the same, although evaluation of the integral is likely to involve more detail.