Given : T = 2500 + 273 = 2773 K ; λ = 12 µm, ε = 0.9
(i) Monochromatic emissive power at 1.2 µm length, (Eλ)b :
According to Planck’s law,
where, C1 = 3.742 × 108 W. µm4/m2 = 0.3742 × 10–15 W.m4/m2 and
C2 = 1.4388 × 10–2 mK
Substituting the values, we get
(ii) Wavelength at which the emission is maximum, λmax :
According to Wien’s displacement law,
(iii) Maximum emissive power, (Eλb)max :
(Eλb)max = 1.285 × 10–5 T5 W/m2 per metre length
= 1.285 × 10–5 × (2773)5 = 2.1 × 1012 W/m2 per metre length.
[Note. At high temperature the difference between (Eλ)b and (Eλb)max is very small].
(iv) Total emissive power, Eb :
Eb = σT4 = 5.67 × 10–8 (2273)4 = 5.67 \(\left(\cfrac{2773}{100}\right)^4\) = 3.352 × 106 W/m2
(v) Total emissive power, E with emisivity (ε) = 0.9
E = ε σT4 = 0.9 × 5.67 \(\left(\cfrac{2773}{100}\right)^4\) = 3.017 × 106 W/m2.