A 100 W beam of light is shone onto a black body of mass2x10^-3 kg for a duratio

Question

A 100 W beam of light is shone onto a black body of mass2x10^-3 kg for a duration of 10^4 s. The black body isinitially at rest in a frictionless space. What is the finalkinetic energy of the black body at the end of the period ofillumination - why is this less than the total energy of theabsorbed photons? A 100 W beam of light is shone onto a black body of mass2x10^-3 kg for a duration of 10^4 s. The black body isinitially at rest in a frictionless space. What is the finalkinetic energy of the black body at the end of the period ofillumination - why is this less than the total energy of theabsorbed photons?

Explanation / Answer

    = 100 W *10000 s = 106 J Now, momentum absorbed by the body = momentum gainedfrom the photons = P = U/c = 106/(3*108)kgm/s = m*v = 2*10-3*v => v = 1.667 m/s
So, kinetic energy gained = 0.5*m*v*v = 2.78*10-3J This value is small because the rest of the radiation energyis used in heating up the black body.

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