Two spherical black bodies of radii $r_1$ and $r_2$ and with surface temperatures $T_1$ and $T_2$ respectively radiate the same power. Then the ratio of $r_1$ and $r_2$ will be:

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.

$A$ body emits $5 \ W$ of energy at a temperature of $127^{\circ}C$. If the temperature is increased to $927^{\circ}C$,then the emitted energy becomes .......... $W$.

$A$ black body radiates $20\,W$ at temperature $227^{\circ}C$. If the temperature of the black body is changed to $727^{\circ}C$,then its radiating power will be ..... $W$.

The temperatures of two bodies $A$ and $B$ are respectively $727^{\circ}C$ and $327^{\circ}C$. The ratio $H_A:H_B$ of the rates of heat radiated by them is

According to Stefan's law of radiation,a black body radiates energy $\sigma T^4$ from its unit surface area every second,where $T$ is the surface temperature of the black body and $\sigma = 5.67 \times 10^{-8} \, W m^{-2} K^{-4}$ is known as Stefan's constant. $A$ nuclear weapon may be thought of as a ball of radius $0.5 \, m$. When detonated,it reaches a temperature of $10^6 \, K$ and can be treated as a black body.
$(a)$ Estimate the power it radiates.
$(b)$ If the surroundings have water at $30 \, ^\circ C$,how much water can $10 \%$ of the energy produced evaporate in $1 \, s$? $[S_W = 4186 \, J kg^{-1} K^{-1}$ and $L_v = 22.6 \times 10^5 \, J kg^{-1}]$
$(c)$ If all this energy $U$ is in the form of radiation,the corresponding momentum is $p = U/c$. How much momentum per unit time does it impart on a unit area at a distance of $1 \, km$?