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(C) According to the Stefan-Boltzmann Law,the total energy radiated per unit time by a black body is given by $E = A \sigma T^4$,where $A$ is the surf

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(C) According to the Stefan-Boltzmann Law,the total energy radiated per unit time by a black body is given by $E = A \sigma T^4$,where $A$ is the surface area,$\sigma$ is the Stefan-Boltzmann constant,and $T$ is the absolute temperature.For a sphere,the surface area $A = 4 \pi r^2$.Therefore,the energy radiated $E \propto r^2 T^4$.The ratio of energy radiated by spheres $P$ and $Q$ is given by:$\frac{E_P}{E_Q} = \left( \frac{r_P}{r_Q} ight)^2 \left( \frac{T_P}{T_Q} ight)^4$.Given: $r_P = 8 \; cm$,$r_Q = 2 \; cm$.Temperatures in Kelvin: $T_P = 127 + 273 = 400 \; K$ and $T_Q = 527 + 273 = 800 \; K$.Substituting the values:$\frac{E_P}{E_Q} = \left( \frac{8}{2} ight)^2 \left( \frac{400}{800} ight)^4 = (4)^2 \left( \frac{1}{2} ight)^4 = 16 	imes \frac{1}{16} = 1$.

Two spheres $P$ and $Q$,of the same color,having radii $8 \; cm$ and $2 \; cm$ are maintained at temperatures $127^{\circ}C$ and $527^{\circ}C$ respectively. The ratio of energy radiated by $P$ and $Q$ is:

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