The adjoining diagram shows the spectral energy density distribution $E_\lambda$ of a black body at two different temperatures. If the areas under the curves are in the ratio $16 : 1$,the value of temperature $T$ is ......... $K$. (in $,000$)

$A$ black metal foil is kept at a distance $d$ from a circular heater. The power absorbed by the foil is $P$. If the temperature of the heater and the distance are both doubled,the power absorbed by the foil will be ..... $P$.

$A$ cube of side $1 \ m$ has a temperature of $127^{\circ}C$ and an emissivity of $\frac{1}{5.67}$. If the surrounding temperature is $27^{\circ}C$,the rate of loss of heat by radiation is ...... $kW$.

$A$ black body of mass $34.38 \ g$ and surface area $19.2 \ cm^2$ is at an initial temperature of $400 \ K$. It is allowed to cool inside an evacuated enclosure kept at a constant temperature of $300 \ K$. The rate of cooling is $0.04 \ ^{\circ}C/s$. The specific heat of the body in $J \ kg^{-1} \ K^{-1}$ is (Stefan's constant $\sigma = 5.73 \times 10^{-8} \ W \ m^{-2} \ K^{-4}$)

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 emits energy at the rate of $1 \ cal/cm^2 \cdot s$ at a temperature of $127^{\circ}C$. Find the rate of energy emission at a temperature of $527^{\circ}C$ in $cal/cm^2 \cdot s$.