$A$ sphere of surface area $4 \ m^2$ at temperature $400 \ K$ and having emissivity $0.5$ is located in an environment of temperature $200 \ K$. The net rate of energy exchange of the sphere is (Stefan-Boltzmann constant $\sigma = 5.67 \times 10^{-8} \ W \ m^{-2} \ K^{-4}$) (in $W$)

Find the rate of energy radiated per minute by an incandescent lamp at $2000 \ K$. The surface area is $5 \times 10^{-5} \ m^{2}$,the emissivity is $0.85$,and $\sigma = 5.7 \times 10^{-8} \ W \ m^{-2} \ K^{-4}$. (in $J$)

$A$ metal ball of surface area $200 \; cm^2$ and temperature $527^{\circ}C$ is surrounded by a vessel at $27^{\circ}C$. If the emissivity of the metal is $0.4$,then the rate of loss of heat from the ball is approximately .......... $J/s$. $(\sigma = 5.67 \times 10^{-8} \; J/(m^2 \cdot s \cdot K^4))$

Two spheres of radii $8 \ cm$ and $2 \ cm$ are cooling. Their temperatures are $127^{\circ} C$ and $527^{\circ} C$ respectively. Find the ratio of energy radiated by them in the same time.

Parallel rays of light of intensity $I = 912 \ W m^{-2}$ are incident on a spherical black body kept in surroundings of temperature $T_0 = 300 \ K$. Take Stefan-Boltzmann constant $\sigma = 5.7 \times 10^{-8} \ W m^{-2} K^{-4}$ and assume that the energy exchange with the surroundings is only through radiation. The final steady state temperature of the black body is close to: (in $K$)

If a substance at temperature $T$ is kept in surroundings at temperature $T_S$,what is the net rate of loss of radiation energy?