The wavelength of maximum intensity of radiation emitted by a star is $289.8 \ nm$. The radiation intensity of the star is (Stefan's constant $= 5.67 \times 10^{-8} \ W m^{-2} K^{-4}$, Wien's constant $b = 2898 \ \mu m \ K$).

$A$ solid cylinder of radius $r_1=2.5 \ cm$, length $l_1=5.0 \ cm$ and temperature $40^{\circ}C$ is suspended in an environment of temperature $60^{\circ}C$. The thermal radiation transfer rate for the cylinder is $1.0 \ W$. If the cylinder is stretched until its radius becomes $r_2=0.50 \ cm$, the thermal radiation transfer rate is changed to (in $W$)

$A$ rectangular metal plate $8 \ cm \times 4 \ cm$ at $127^{\circ} C$ emits $E \ Js^{-1}$. If both length and breadth are halved and the temperature is raised to $327^{\circ} C$,the rate of emission is

$A$ black body emits energy at the rate of $1.0 \times 10^{6} \ J/s \cdot m^{2}$ at $127^{\circ}C$. At what temperature will the energy emission rate be $16.0 \times 10^{6} \ J/s \cdot m^{2}$ in $^{\circ}C$?

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

The area of a hole of a heat furnace is $10^{-4} \ m^2$. It radiates $1.58 \times 10^5 \ \text{calories}$ of heat per hour. If the emissivity of the furnace is $0.80$, then its temperature is ....... $K$.