$A$ black body at a temperature of $227^{\circ} C$ radiates heat energy at the rate of $5 \ cal/cm^{2}-s$. At a temperature of $727^{\circ} C$,the rate of heat radiated per unit area in $cal/cm^{2}-s$ will be:

The amount of heat energy radiated by a metal at temperature $T$ is $E$. When the temperature is increased to $3T$,the energy radiated is: (in $E$)

$A$ 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 $\sigma = 5.67 \times 10^{-8} \ W m^{-2} K^{-4}$):

Calculate the surface temperature of the planet,if the energy radiated by unit area in unit time is $5.67 \times 10^4 \, W$. (Assume the planet to be a black body).

The actual temperature of a black body is $727^{\circ}C$. At what temperature in $K$ will the black body emit twice the radiation?

The energy spectrum of a black body exhibits a maximum around a wavelength $\lambda$. The temperature of a black body is now changed such that the energy is maximum at wavelength $2\lambda/3$. The power radiated by the black body will now increase by a factor of