If $E$ is the total energy emitted by a body at temperature $T \ K$ and $E_{max}$ is the maximum energy emitted by it at the same temperature,then:

The filament of a light bulb has a surface area of $64 \ mm^2$. The filament can be considered as a black body at a temperature of $2500 \ K$,emitting radiation like a point source when viewed from afar. At night,the light bulb is observed from a distance of $100 \ m$. Assume the pupil of the observer's eye to be circular with a radius of $3 \ mm$. Then:
(Take Stefan-Boltzmann constant $= 5.67 \times 10^{-8} \ W \ m^{-2} \ K^{-4}$,Wien's displacement constant $= 2.90 \times 10^{-3} \ m \ K$,Planck's constant $= 6.63 \times 10^{-34} \ J \ s$,speed of light in vacuum $= 3.00 \times 10^8 \ m \ s^{-1}$)
$(A)$ The power radiated by the filament is in the range $642 \ W$ to $645 \ W$.
$(B)$ The radiated power entering into one eye of the observer is in the range $3.15 \times 10^{-8} \ W$ to $3.25 \times 10^{-8} \ W$.
$(C)$ The wavelength corresponding to the maximum intensity of light is $1160 \ nm$.
$(D)$ Taking the average wavelength of emitted radiation to be $1740 \ nm$,the total number of photons entering per second into one eye of the observer is in the range $2.75 \times 10^{11}$ to $2.85 \times 10^{11}$.

Heat travels through vacuum by

Three very large plates of the same area are kept parallel and close to each other. They are considered as ideal black surfaces and have very high thermal conductivity. The first and third plates are maintained at temperatures $2\ T$ and $3\ T$ respectively. The temperature of the middle (i.e.,second) plate under steady-state condition is

If the absorptance and reflectance of a surface are $0.4$ and $0.6$ respectively,then:

Select the incorrect statement.