The radiated power of a body at $400 \,K$ is $1000 \,W$. If the temperature is raised to $800 \,K$, what would be the radiated power of the body (in $W$)?

Two spheres $S_{1}$ and $S_{2}$ have radii $R$ and $3R$ and temperatures $T$ and $T/3$ respectively. If they are coated with a material of the same emissivity, and the rate of radiation of $S_{1}$ is $E$, then the rate of radiation of $S_{2}$ is:

The Sun emits electromagnetic energy at a rate of $3.9 \times 10^{25} \ W$. Its radius is $6.96 \times 10^8 \ m$. The intensity of sunlight at the solar surface in $W \ m^{-2}$ is:

$A$ sphere of surface area $4 \ m^2$ at temperature $400 \ K$ and having emissivity $0.5$ is located in an environment of temperature $200 \ K$. The net rate of energy exchange of the sphere is (Stefan-Boltzmann constant $\sigma = 5.67 \times 10^{-8} \ W \ m^{-2} \ K^{-4}$) (in $W$)

$A$ spherical black body of radius $r$ radiates power $P$ and its rate of cooling is $R$. Which of the following relations are correct?
$(i) \ P \propto r$
$(ii) \ P \propto r^2$
$(iii) \ R \propto r^2$
$(iv) \ R \propto \frac{1}{r}$

$A$ black body at $227^o C$ radiates heat at the rate of $7 \; cal/cm^2 s$. At a temperature of $727^o C$,the rate of heat radiated in the same units will be: