Write the value and dimensional formula of the Stefan-Boltzmann constant.

$A$ black sphere has radius $R$ whose rate of radiation is $E$ at temperature $T$. If the radius is made half and the temperature is made $4T$,the rate of radiation will be: (in $E$)

$A$ black body is at a temperature $300 K$. It emits energy at a rate,which is proportional to

An object is at a temperature of $400^{\circ}C$. At what temperature would it radiate energy twice as fast? The temperature of the surroundings may be assumed to be negligible.

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?

Assume that the solar constant is $1.4 \, kW/m^2$,the radius of the sun is $7 \times 10^5 \, km$,and the distance of the earth from the center of the sun is $1.5 \times 10^8 \, km$. Given Stefan's constant is $\sigma = 5.67 \times 10^{-8} \, W m^{-2} K^{-4}$,find the approximate temperature of the sun in $K$.