The temperature of a black body reduces to half of its initial value. By what fraction will the amount of radiation emitted reduce?

State and explain the Stefan-Boltzmann law.

$A$ black coloured solid sphere of radius $R$ and mass $M$ is inside a cavity with vacuum inside. The walls of the cavity are maintained at temperature $T_0$. The initial temperature of the sphere is $3T_0$. If the specific heat of the material of the sphere varies as $\alpha T^3$ per unit mass with the temperature $T$ of the sphere,where $\alpha$ is a constant,then the time taken for the sphere to cool down to temperature $2T_0$ will be ($\sigma$ is Stefan-Boltzmann constant).

$A$ body radiates energy at a rate of $5 \ W$ at a temperature of $127^{\circ}C$. If the temperature is increased to $927^{\circ}C$,then it radiates energy at the rate of ...... $W$.

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

$A$ black rectangular surface of area $A$ emits energy $E$ per second at $27^{\circ} C$. If length and breadth are reduced to $1/3$ of their initial values and the temperature is raised to $327^{\circ} C$,then the energy emitted per second becomes: