The temperature of a black body reduces to half of its initial value. By what fraction will the amount of radiation emitted reduce?

$A$ black body of mass $34.38 \ g$ and surface area $19.2 \ cm^2$ is at an initial temperature of $400 \ K$. It is allowed to cool inside an evacuated enclosure kept at a constant temperature of $300 \ K$. The rate of cooling is $0.04 \ ^{\circ}C/s$. The specific heat of the body in $J \ kg^{-1} \ K^{-1}$ is (Stefan's constant $\sigma = 5.73 \times 10^{-8} \ W \ m^{-2} \ K^{-4}$)

The emissivity (power radiated per unit area) of a perfect black body is increased to $16$ times by increasing its temperature. If the initial temperature is $T$, then the final temperature of that black body is: (in $\,T$)

Two spheres of the same material have radii $1 \ m$ and $4 \ m$ and temperatures $4000 \ K$ and $2000 \ K$ respectively. The ratio of the energy radiated by them is .....

$A$ certain stellar body has radius $50 \,R_{s}$ and temperature $2 \,T_{s}$ and is at a distance of $2 \times 10^{10} \,AU$ from the earth. Here,$AU$ refers to the earth-sun distance and $R_{s}$ and $T_{s}$ refer to the sun's radius and temperature,respectively. Take both the star and the sun to be ideal black bodies. The ratio of the power received on earth from the stellar body as compared to that received from the sun is close to

$A$ sphere at temperature $600\,K$ is placed in an environment of temperature $200\,K$. Its cooling rate is $H$. If its temperature is reduced to $400\,K$,then the cooling rate in the same environment will become: