$A$ hot metallic sphere of radius $r$ radiates heat. Its rate of cooling is

$A$ sphere is at temperature $600 \ K$. In an external environment of $200 \ K$,its cooling rate is $R$. When the temperature of the sphere falls to $400 \ K$,then the cooling rate $R'$ will become:

The operating temperature and emissivity of a tungsten filament are $2000 \ K$ and $0.3$,respectively. The surface area of the filament is $A \ cm^2$. If the power of the lamp is $25 \ W$,find $A$. (Given: $\sigma = 5.67 \times 10^{-8} \ W/m^2K^4$)

Three very large plates of the same area are kept parallel and close to each other. They are considered as ideal black surfaces and have very high thermal conductivity. The first and third plates are maintained at temperatures $2T$ and $3T$ respectively. The temperature of the middle (i.e.,second) plate under steady-state condition 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.

$A$ black body radiates energy at the rate of $E \text{ W/m}^2$ at a high temperature $T \text{ K}$. When the temperature is reduced to $\left(\frac{T}{2}\right) \text{ K}$, the radiant energy is