What will be the fractional increase in radiant energy?

Question

A lamp is designed to operate at a temperature of 3050K. If the lamp is operated at a higher voltage that raises its temperature to 3600K, what will be the fractional increase in radiant energy?

I need the equation please and an explanation. thanks

Answer 1

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black body radiators emit energy according to

E = sigma T^4 where sigma is a constant

the temperature increase here is 3600/3050=1.18

so the energy increases by 1.18^4=1.94 times