If the temperature of a black body is increased from $27^{\circ}C$ to $327^{\circ}C$,the radiation emitted increases by a factor of:

The operating temperature and emissivity of a tungsten filament are $2000 \ K$ and $0.3$,respectively. The surface area of the filament is $A \ cm^2$. If the power of the lamp is $25 \ W$,find $A$. (Given: $\sigma = 5.67 \times 10^{-8} \ W/m^2K^4$)

The distance between the Sun and the Earth is $2 \times 10^{8} \ km$, the temperature of the Sun is $6000 \ K$, and the radius of the Sun is $7 \times 10^{5} \ km$. If the emissivity of the Earth is $0.6$, find the temperature of the Earth in thermal equilibrium (in $K$).

The amount of heat energy radiated by a metal at temperature $T$ is $E$. When the temperature is increased to $3T$,the energy radiated is: (in $E$)

Two identical bodies have temperatures $277^{\circ} C$ and $67^{\circ} C$. If the surroundings temperature is $27^{\circ} C$, the ratio of loss of heats of the two bodies during the same interval of time is (approximately) (in $ : 1$)

The total energy radiated from a black body source is collected for one minute and is used to heat a quantity of water. The temperature of water is found to increase from $20^{\circ}C$ to $20.5^{\circ}C$. If the absolute temperature of the black body is doubled and the experiment is repeated with the same quantity of water at $20^{\circ}C$,the temperature of water will be....... $^{\circ}C$