The filament of a light bulb has surface area 64 mm 2 . The filament can be considered as a black body at temperature 2500 K emitting radiation like a point source when viewed from far. At night the light bulb is observed from a distance of 100 m . Assume the pupil of the eyes of the observer to be circular with radius 3 mm . Then: (Take Stefan-Boltzmann constant = 5 . 67 × 10 - 8 W m - 2 K - 4 , Wiens' displacement constant = 2 .90 × 10 − 3 m K , Planck's constant = 6 .60 × 10 − 34 J s , speed of light in vacuum = 3 .00 × 10 8 m s − 1 )

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 × 10 11 to 2 . 85 × 10 11

power radiated by the filament is in the range 642 W to 645 W

A human body has a surface area of approximately 1 m 2 . The normal body temperature is 10 K above the surrounding room temperature T 0 . Take the room temperature to be T 0 = 300 K . For T 0 = 300 K , the value of σ T 4 = 460 W m - 2 (where σ is the Stefan-Boltzmann constant). Which of the following options is/are correct?

Reducing the exposed surface area of the body (e.g. by curling up) allows humans to maintain the same body temperature while reducing the energy lost by radiation.

If the surrounding temperature reduces by a small amount Δ T 0 < < T 0 , then to maintain the same body temperature the same (living) human being needs to radiate Δ W = 4 σ T 0 3 Δ T 0 more energy per unit time

If the body temperature rises significantly then the peak in the spectrum of electromagnetic radiation emitted by the body would shift to longer wavelengths