If the temperature of the Sun gets doubled, the rate of energy received on the Earth will increase by a factor of

$A$ thin steel square plate of side $10 \ cm$ is heated. The rate of energy emission from the heated plate is $1134 \ W$. What is the temperature of the plate in $K$? (Assume emissivity $\varepsilon = 1$ and $\sigma = 5.67 \times 10^{-8} \ W \ m^{-2} \ K^{-4}$)

The top of an insulated cylindrical container is covered by a disc having emissivity $0.6$ and thickness $1\, cm$. The temperature is maintained by circulating oil as shown in the figure. If the temperature of the upper surface of the disc is $127^\circ C$ and the temperature of the surroundings is $27^\circ C$,then the radiation loss to the surroundings will be (Take $\sigma = \frac{17}{3} \times 10^{-8} \, W/m^2 K^4$)

If the radius of a star is $R$ and it acts as a black body,what would be the temperature of the star,in which the rate of energy production is $Q$? ($\sigma$ stands for Stefan's constant)

$A$ 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 $\sigma = 5.73 \times 10^{-8} \ W \ m^{-2} \ K^{-4}$)

Two spherical black bodies of radius $r_{1}$ and $r_{2}$ with surface temperatures $T_{1}$ and $T_{2}$ respectively,radiate the same power. Then the ratio $r_{1}: r_{2}$ is: