$A$ perfectly black body emits radiation at a temperature $T_1 \ K$. If it is to radiate at $16$ times this power,its temperature $T_2 \ K$ should be: (in $T_1$)

$A$ 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 $x$.

$A$ black body radiates energy at the rate of $E \text{ W/m}^2$ at a high temperature $T \text{ K}$. When the temperature is reduced to $\left(\frac{T}{2}\right) \text{ K}$, the radiant energy is

Two spherical black bodies of radius $r_{1}$ and $r_{2}$ with surface temperatures $T_{1}$ and $T_{2}$ respectively,radiate the same power. Then the ratio $r_{1}: r_{2}$ is:

$A$ thin square steel plate with each side equal to $10$ cm is heated by a blacksmith. The rate of radiated energy by the heated plate is $1134$ $W$. The temperature of the hot steel plate is ....... $K$ (Stefan's constant $\sigma = 5.67 \times 10^{-8} \text{ W m}^{-2} \text{ K}^{-4}$,emissivity of the plate = $1$).

$A$ tungsten body of diameter $2.3 \ cm$ is at $2000 \ ^oC$. It radiates $30 \%$ of the energy radiated by a black body of the same radius and temperature. Find the radius of a black body which will radiate energy at the same rate at the same temperature (in $cm$).