A human body has a surface area of approximately 1 m2. The normal body temperature is 10 K above the surrounding room temperature T0. Take the room temperature to be T0=300 K. For T0=300 K, the value of σT04=460 Wm−2 ( where σ is the Stefan Boltzmann constant). Which of the following options is/are correct? Assume human beings to be black body.
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a
If the body temperature rises significantly then the peak in the spectrum of electromagnetic radiation emitted by the body would shift to longer wavelengths
b
If the surrounding temperature reduces by a small amount ΔT0<
c
The amount of energy radiated by the body in 1 second is close to 60 joules
d
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
answer is D.
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Detailed Solution
(A) is clearly wrong from Wien’s displacement law.(B) For black body e=1 Initial radiated power : W1=σAT4−T04Final radiated power : W2=σAT4−T0−ΔT04Extra power radiated : W2−W1=4σAT03ΔT0 (C) For black body e=1 W2−W1=4σAT03ΔT0=4×460300×10=61 J in 1secAs human body is not a black body , Options (B) and (C) are wrong.(D) True, by reducing area, net power emitted is reduced while his body will produce same heat inside so will be easy to maintain temperature.
A human body has a surface area of approximately 1 m2. The normal body temperature is 10 K above the surrounding room temperature T0. Take the room temperature to be T0=300 K. For T0=300 K, the value of σT04=460 Wm−2 ( where σ is the Stefan Boltzmann constant). Which of the following options is/are correct? Assume human beings to be black body.