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 plots of intensity $(I)$ versus wavelength $(\lambda)$ for three black bodies at temperatures $T_1, T_2$ and $T_3$ respectively are as shown. Their temperatures are such that:

Observations of light from three different stars $A, B$,and $C$ show that the intensity of the red color is maximum for star $A$,the intensity of the blue color is maximum for star $B$,and the intensity of the yellow color is maximum for star $C$. Which of the following conclusions can be drawn from these observations?

The wavelength of maximum intensity of radiation emitted by a star is $289.8 \, nm$. The radiation intensity of the star is (Stefan's constant $\sigma = 5.67 \times 10^{-8} \, W m^{-2} K^{-4}$, Wien's constant $b = 2898 \, \mu m K$).

$A$ 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:

Which graph represents the $v_m - T$ relationship for a black body,where $v_m$ is the frequency corresponding to the maximum energy emission and $T$ is the absolute temperature?