$A$ black body at $227^{\circ}C$ radiates heat at the rate of $20 \, cal \, m^{-2} \, s^{-1}$. When its temperature is raised to $727^{\circ}C$,the rate of heat radiation will be $x \, cal \, m^{-2} \, s^{-1}$. Find $x$.

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.

The temperature at which a black body of unit area loses its energy at the rate of $1 \text{ J/s}$ is:

Two spheres of same material and radii $5 \ m$ and $2 \ m$ are at temperatures $200 \ K$ and $250 \ K$ respectively. The ratio of energies radiated by them per second is

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

An electric heater kept in a vacuum is heated continuously by passing an electric current. Its temperature: