Two spheres P and Q have the same emissivity | vedclass

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(C) The radiant energy emitted per unit time by a sphere is given by Stefan-Boltzmann Law: $E = \sigma A T^4$,where $A = 4\pi r^2$.Thus,the ratio of r

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(C) The radiant energy emitted per unit time by a sphere is given by Stefan-Boltzmann Law: $E = \sigma A T^4$,where $A = 4\pi r^2$.Thus,the ratio of radiant energy emitted by $P$ and $Q$ is given by:$\frac{E_P}{E_Q} = \frac{\sigma (4\pi r_P^2) T_P^4}{\sigma (4\pi r_Q^2) T_Q^4} = \left( \frac{r_P}{r_Q} ight)^2 	imes \left( \frac{T_P}{T_Q} ight)^4$Given: $r_P = 8 \ cm$,$r_Q = 2 \ cm$,$T_P = 127 + 273 = 400 \ K$,$T_Q = 527 + 273 = 800 \ K$.Substituting the values:$\frac{E_P}{E_Q} = \left( \frac{8}{2} ight)^2 	imes \left( \frac{400}{800} ight)^4$$\frac{E_P}{E_Q} = (4)^2 	imes \left( \frac{1}{2} ight)^4 = 16 	imes \frac{1}{16} = 1$.Therefore,the ratio is $1:1$.

Two spheres $P$ and $Q$ have the same emissivity and radii $8 \ cm$ and $2 \ cm$ respectively. They are maintained at temperatures $127^{\circ}C$ and $527^{\circ}C$ respectively. Find the ratio of the radiant energy emitted by $P$ to that by $Q$.

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