At what temperature $T$ (in $K$) will a perfectly black body radiate energy at the rate of $5.67 \, W \, cm^{-2}$ (in $, K$)? Given Stefan's constant $\sigma = 5.67 \times 10^{-8} \, W \, m^{-2} K^{-4}$.

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 per second by the first sphere to that by the second is

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.

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 $1 \, km$?

$A$ black body,at a temperature of $227\,^{\circ}C$,radiates heat at a rate of $7\, cal\, cm^{-2} \,s^{-1}$. At a temperature of $727\,^{\circ}C$,the rate of heat radiated in the same units will be ..... units.

$A$ black body is at a temperature of $500 \; K$. It emits energy at a rate which is proportional to: