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15 marks The black body radiation spectrum for the power p.pdf

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[15 marks] The black body radiation spectrum for the power per square metre of the surface of the radiating body at wavelength and temperature T is E(,T)=52hc2(ekThc11) where h is Planck's constant, c is the speed of light and k is Boltzmann's constant. Thus the power per unit area emitted from the surface with wavelengths in an interval [a,b] is abE(,T)d, and if is in some small range about c the total emission is approximately E(c,T) Show that the ratio of the power from the Earth to the power from the Sun in a waveband about c in the Earth's atmosphere is approximately Q=(R02re2)ekcTehc1ekcT0hc1 where R0 is the radius of the Sun, re is the radius of the Earth's orbit, T0 is the temperature of the Sun and Te is the temperature of the Earth..

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[15 marks] The black body radiation spectrum for the power per square metre of the surface of the radiating body at wavelength and temperature T is E(,T)=52hc2(ekThc11) where h is Planck's constant, c is the speed of light and k is Boltzmann's constant. Thus the power per unit area emitted from the surface with wavelengths in an interval [a,b] is abE(,T)d, and if is in some small range about c the total emission is approximately E(c,T) Show that the ratio of the power from the Earth to the power from the Sun in a waveband about c in the Earth's atmosphere is approximately Q=(R02re2)ekcTehc1ekcT0hc1 where R0 is the radius of the Sun, re is the radius of the Earth's orbit, T0 is the temperature of the Sun and Te is the temperature of the Earth.

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  • 1. [15 marks] The black body radiation spectrum for the power per square metre of the surface of the radiating body at wavelength and temperature T is E(,T)=52hc2(ekThc11) where h is Planck's constant, c is the speed of light and k is Boltzmann's constant. Thus the power per unit area emitted from the surface with wavelengths in an interval [a,b] is abE(,T)d, and if is in some small range about c the total emission is approximately E(c,T) Show that the ratio of the power from the Earth to the power from the Sun in a waveband about c in the Earth's atmosphere is approximately Q=(R02re2)ekcTehc1ekcT0hc1 where R0 is the radius of the Sun, re is the radius of the Earth's orbit, T0 is the temperature of the Sun and Te is the temperature of the Earth.