$A$ 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 $T_1$)

Two black spheres $P$ and $Q$ have radii in the ratio $4:3$. The wavelengths of maximum intensity of radiation are in the ratio $4:5$ respectively. The ratio of radiated power by $P$ to $Q$ is

The total energy of a black body radiation source is collected for five minutes and used to heat water. The temperature of the water increases from $10.0^{\circ} C$ to $11.0^{\circ} C$. The absolute temperature of the black body is doubled and its surface area halved and the experiment repeated for the same time. Which of the following statements would be most nearly correct?

Radiated energy at $T$ temperature is $E$ for a body of diameter $d$. If the temperature becomes $2T$ and the diameter becomes $d/4$,then the radiated energy will be:

Two spherical bodies of same materials having radii $0.2 \ m$ and $0.8 \ m$ are placed in the same atmosphere. The temperature of the smaller body is $800 \ K$ and the temperature of the bigger body is $400 \ K$. If the energy radiated from the smaller body is $E$,the energy radiated from the bigger body is (assume the effect of the surrounding to be negligible).

$A$ black rectangular surface of area $A$ emits energy $E$ per unit time at $27^{\circ}C$. If length and breadth are reduced to $(1/4)^{th}$ of their initial values and the temperature is raised to $327^{\circ}C$, then the energy emitted per unit time becomes: