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(C) The energy radiated by a body is given by Stefan-Boltzmann Law: $Q = A \varepsilon \sigma T^{4} t$.Since the time $t$,emissivity $\varepsilon$,and

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$1$

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(C) The energy radiated by a body is given by Stefan-Boltzmann Law: $Q = A \varepsilon \sigma T^{4} t$.Since the time $t$,emissivity $\varepsilon$,and Stefan-Boltzmann constant $\sigma$ are the same for both,the energy radiated $Q$ is proportional to $A T^{4}$.Since $A = 4 \pi r^{2}$,we have $Q \propto r^{2} T^{4}$.The temperatures must be in Kelvin: $T_{1} = 127 + 273 = 400 \ K$ and $T_{2} = 527 + 273 = 800 \ K$.The ratio of energy radiated is:$\frac{Q_{1}}{Q_{2}} = \left(\frac{r_{1}}{r_{2}}ight)^{2} \left(\frac{T_{1}}{T_{2}}ight)^{4}$$\frac{Q_{1}}{Q_{2}} = \left(\frac{8}{2}ight)^{2} \left(\frac{400}{800}ight)^{4}$$\frac{Q_{1}}{Q_{2}} = (4)^{2} 	imes \left(\frac{1}{2}ight)^{4}$$\frac{Q_{1}}{Q_{2}} = 16 	imes \frac{1}{16} = 1$.

Two spheres of radii $8 \ cm$ and $2 \ cm$ are cooling. Their temperatures are $127^{\circ} C$ and $527^{\circ} C$ respectively. Find the ratio of energy radiated by them in the same time.

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