If the temperature of a black body increases from $7\,^{\circ}C$ to $287\,^{\circ}C$,then the rate of energy radiation increases by

What is the ratio of energy emitted by a black body at temperatures $27^{\circ}C$ and $927^{\circ}C$?

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

The distance between the Sun and the Earth is $2 \times 10^{8} \ km$, the temperature of the Sun is $6000 \ K$, and the radius of the Sun is $7 \times 10^{5} \ km$. If the emissivity of the Earth is $0.6$, find the temperature of the Earth in thermal equilibrium (in $K$).

$A$ 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 $cal/cm^2 \cdot s$.

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 the radius of the Earth is $r_0$).