$A$ black body emits energy at the rate of $1 \ cal/cm^2 \cdot s$ at a temperature of $127^{\circ}C$. Find the rate of energy emission at a temperature of $527^{\circ}C$ in $cal/cm^2 \cdot s$.

$A$ black body surface with an area of $8 \ cm \times 4 \ cm$ emits energy at a rate of $E$ per second at a temperature of $127^{\circ}C$. If the length and width are halved and the temperature is increased to $327^{\circ}C$,find the new rate of energy emission.

$A$ sphere and a cube,both made of copper,have equal volumes and are black. They are allowed to cool at the same temperature and in the same atmosphere. The ratio of their rate of loss of heat is:

$A$ small object is placed at the center of a large evacuated hollow spherical container. Assume that the container is maintained at $0 \ K$. At time $t = 0$,the temperature of the object is $200 \ K$. The temperature of the object becomes $100 \ K$ at $t = t_1$ and $50 \ K$ at $t = t_2$. Assume the object and the container to be ideal black bodies. The heat capacity of the object does not depend on temperature. The ratio $(t_2 / t_1)$ is:

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

$A$ black rectangular surface of area $A$ emits energy $E$ per second at $127^\circ C$. If length and breadth are reduced to half of their initial values and the temperature is raised to $527^\circ C$, then the energy emitted becomes: