Power radiated by a black body at temperature $T_1$ is $P$ and it radiates maximum energy at a wavelength $\lambda_1$. If the temperature of the black body is changed from $T_1$ to $T_2$, it radiates maximum energy at a wavelength $\frac{\lambda_1}{2}$. The power radiated at $T_2$ is (in $P$)

Three discs $A, B$ and $C$ having radii $2\; m, 4\; m,$ and $6\; m$ respectively are coated with carbon black on their outer surfaces. The wavelengths corresponding to maximum intensity are $300\; nm, 400\; nm$ and $500\; nm$ respectively. The power radiated by them are $Q_A, Q_B$ and $Q_C$ respectively. Which of the following is true?

Two bodies $A$ and $B$ have thermal emissivities of $0.01$ and $0.81$ respectively. The outer surface areas of the two bodies are the same. The two bodies emit total radiant power at the same rate. The wavelength ${\lambda _B}$ corresponding to maximum spectral radiancy in the radiation from $B$ is shifted from the wavelength corresponding to maximum spectral radiancy in the radiation from $A$ by $1.00\;\mu m$. If the temperature of $A$ is $5802\;K$,then:

Two rods (one semi-circular and other straight) of the same material and of the same cross-sectional area are joined as shown in the figure. The points $A$ and $B$ are maintained at different temperatures. The ratio of the heat transferred through a cross-section of the semi-circular rod to the heat transferred through a cross-section of the straight rod in a given time is

$A$ black body radiates maximum energy at wavelength $\lambda$ and its emissive power is $E$. Now, due to a change in the temperature of that body, it radiates maximum energy at wavelength $\frac{2 \lambda}{3}$. At that temperature, the emissive power is:

The sun,acting as a black body,emits maximum radiation at a wavelength of $0.48 \ \mu m$. The average radius of the sun is $6.96 \times 10^{8} \ m$. The Stefan-Boltzmann constant is $5.67 \times 10^{-8} \ W/m^2K^4$ and Wien's constant is $0.293 \ cm \cdot K$. The decrease in the mass of the sun per second due to radiation is ..... $kg/s$.