If the temperature of a perfectly black body is increased by $50\%$,find the percentage increase in the amount of radiation emitted from its surface.

Two bodies $A$ and $B$ at temperatures $T_1 \ K$ and $T_2 \ K$ respectively have the same dimensions. Their emissivities are in the ratio $16:1$. At $T_1 = x T_2$,they radiate the same amount of heat per unit area per unit time. The value of $x$ is

If the temperature of the sun is doubled,the rate of energy received by the earth will be increased by a factor of:

The radiation emitted by a star $A$ is $10000$ times that of the sun. If the surface temperatures of the sun and the star $A$ are $6000 \ K$ and $2000 \ K$ respectively,the ratio of the radii of the star $A$ and the sun is: (in $: 1$)

The power radiated by a black body is $P$ and it radiates maximum energy at wavelength $\lambda_0$. If the temperature of the black body is now changed so that it radiates maximum energy at wavelength $\frac{3}{4}\lambda_0$,the power radiated by it becomes $nP$. The value of $n$ is

Two spheres of the same material have radii $1 \ m$ and $4 \ m$ and temperatures $4000 \ K$ and $2000 \ K$ respectively. The energy radiated per second by the first sphere is