The total energy radiated from a black body source is collected for one minute and is used to heat a quantity of water. The temperature of water is found to increase from $20^{\circ}C$ to $20.5^{\circ}C$. If the absolute temperature of the black body is doubled and the experiment is repeated with the same quantity of water at $20^{\circ}C$,the temperature of water will be....... $^{\circ}C$

If the sun's surface radiates heat at $6.3 \times 10^7 \ W m^{-2}$,calculate the temperature of the sun assuming it to be a black body $(\sigma = 5.7 \times 10^{-8} \ W m^{-2} K^{-4})$.

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 coloured solid sphere of radius $R$ and mass $M$ is inside a cavity with vacuum inside. The walls of the cavity are maintained at temperature $T_0$. The initial temperature of the sphere is $3T_0$. If the specific heat of the material of the sphere varies as $\alpha T^3$ per unit mass with the temperature $T$ of the sphere,where $\alpha$ is a constant,then the time taken for the sphere to cool down to temperature $2T_0$ will be ($\sigma$ is Stefan-Boltzmann constant).

$A$ black metal foil is kept at a distance $d$ from a circular heater. The power absorbed by the foil is $P$. If the temperature of the heater and the distance are both doubled,the power absorbed by the foil will be ..... $P$.

Assuming the Sun to be a spherical body of radius $R$ at a temperature of $T \ K$,evaluate the total radiant power incident on Earth at a distance $r$ from the Sun. Where $r_0$ is the radius of the Earth and $\sigma$ is Stefan's constant.