For a black body at temperature $727^{\circ} C$,its radiating power is $60\; W$ and the temperature of the surrounding is $227^{\circ} C$. If the temperature of the black body is changed to $1227^{\circ} C$,then its radiating power will be ..... $W$.

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 $1 \, km$?

Two black bodies at temperatures $327^{\circ} C$ and $427^{\circ} C$ are kept in an evacuated chamber at $27^{\circ} C$. The ratio of their rates of loss of heat are :

In an external environment of temperature $T$ Kelvin, a sphere at temperature $3T$ Kelvin has a cooling rate $R_1$. When the temperature of that sphere falls to $2T$ Kelvin, the cooling rate of the sphere will become:

$A$ very small hole in an electric furnace is used for heating metals. The hole nearly acts as a black body. The area of the hole is $200 \ mm^2$. To keep a metal at $727^{\circ} C$, the heat energy flowing through this hole per second, in joules, is (given $\sigma = 5.67 \times 10^{-8} \ W m^{-2} K^{-4}$):

The energy emitted by a black body at $27^{\circ}C$ is $10 \ J$. If the temperature of the black body is increased to $327^{\circ}C$,the rate of energy emission per second will be ...... $J$.