If the temperature of the Sun gets doubled, the rate of energy received on the Earth will increase by a factor of

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 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.

$A$ black body surface with an area of $8 \ cm \times 4 \ cm$ emits energy at a rate of $E$ per second at a temperature of $127^{\circ}C$. If the length and width are halved and the temperature is increased to $327^{\circ}C$,find the new rate of energy emission.

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

The energy spectrum of a black body exhibits a maximum of wavelength $\lambda_0$. The temperature of the black body is now changed such that the energy is maximum at wavelength $\frac{3\lambda_0}{2}$. The ratio of power radiated by the black body will be