The wavelength of the radiation emitted by a black body is $1 \,mm$ and Wien's constant is $3 \times 10^{-3} \,mK$. Then the temperature of the black body will be (in $\,K$)

The wavelength of maximum emission from a body at a temperature of $200 \, K$ is $14 \, \mu m$. If the temperature of the body is increased to $1000 \, K$,find the new wavelength of maximum emission.

The temperature of a furnace is $2000^\circ C$ and the wavelength of maximum intensity in its spectrum is $4000 \ \mathring{A}$. If the wavelength of maximum intensity is $2000 \ \mathring{A}$, calculate the temperature of the furnace in $^\circ C$.

The graph of relative intensity versus wavelength for three perfectly black bodies at temperatures $T_1, T_2,$ and $T_3$ is shown below. The relationship between their temperatures is:

Two spherical bodies $A$ (radius $6 \,cm$) and $B$ (radius $18 \,cm$) are at temperatures $T_1$ and $T_2$,respectively. The maximum intensity in the emission spectrum of $A$ is at $500 \,nm$ and in that of $B$ is at $1500 \,nm$. Considering them to be black bodies,what will be the ratio of the rate of total energy radiated by $A$ to that of $B$?

For a perfectly black body,a graph is plotted between the frequency of radiation with maximum intensity $(v_m)$ and the absolute temperature $T$. Which of the following graphs is correct?