Question

In a certain instant a body with radiation has a temperature To (kelvin), and its surroundings release a temperature of 500K (To>500K). Then, the temperature of radiation of the body increases to 3To y and heat flow increases in a 333 factor. What is the value of the original temprature of the body To?

Answer 1

Heat flow when the temperature of the source is T_o
q₁ = (T_o⁴ - 500⁴) ------------(1)
Where is the stefan boltzaman constant
Now when the temperature is changed to 3T_o
q₂ = *[(3T_o)⁴ - 500⁴]
It is given that q₂ = 333q₁ , therefore
333q₁ =  *[(3T_o)⁴ - 500⁴] ---------------(2)
On dividing 2 by 1
333 *(T_o⁴ - 500⁴) = [(3T_o)⁴ - 500⁴]
333T_o⁴ - 333*500⁴ = 81T_o⁴ -500⁴
(333 -81)T_o⁴ = (333-1)*500⁴
252*T_o⁴ = 332*500⁴
T_o = 535.678 K
Hence this would be the original temperature of the body