The rate of radiation by a black body is $R$ at temperature $T$. Another body has the same area but an emissivity of $0.2$ and a temperature of $3T$. Its rate of radiation is: (in $R$)

$A$ wire of length $10 \ cm$ and diameter $0.5 \ mm$ is used in a bulb. The temperature of the wire is $1727^{\circ} C$ and power radiated by the wire is $94.2 \ W$. Its emissivity is $\frac{x}{8}$ where $x=$ . . . . . . (Given $\sigma=6.0 \times 10^{-8} \ W \ m^{-2} \ K^{-4}$,$\pi=3.14$ and assume that the emissivity of wire material is same at all wavelengths.)

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

The outer surface of a star in the form of a sphere radiates heat as a black body at temperature $T$. The total radiant energy per unit area,normal to the direction of incidence,received at a distance $R$ from the center of a star of radius $r$ is $(R > r)$ ($\sigma =$ Stefan's constant).

$A$ black body is at a temperature of $500 \; K$. It emits energy at a rate which is proportional to:

The temperature of a black body is increased by $50 \%$. The percentage increase in the rate of radiation by the body is approximately: (in $\%$)