$A$ spherical black body with a radius of $12 \ cm$ radiates $450 \ W$ power at $500 \ K$. If the radius were halved and the temperature doubled,the power radiated in watt would be

$A$ tungsten body of diameter $2.3 \ cm$ is at $2000 \ ^oC$. It radiates $30 \%$ of the energy radiated by a black body of the same radius and temperature. Find the radius of a black body which will radiate energy at the same rate at the same temperature (in $cm$).

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 ....... $K$.

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 $K$.

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

If the temperature of the sun (black body) is doubled,the rate of energy received on earth will be increased by a factor of