A black body with surface area 0.001 `m^(2)` is heated upto a temperature 400 K and is suspended in a room temperature 300K. The intitial rate of loss of heat from the body to room is

Options

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 reduced by a small amount `DeltaT_(0)ltltT_(0)` , then to maintain the same body temperature the same (living) human being needs to radiate `DeltaW=4sigmaT_(0)^(3)DeltaT_(0)` more energy per unit time
C. The amount of energy radiated by the body in 1s is close to 60 J
D. Reducing the exposed surface area of the body (e.g. by curling up) allows humans

Answer

D

Explanation

Assumption `in=1` [black body radiation]
Power `P=sigmaA(T^(4)-T_(0)^(4))`
(C ) `P_("rad")=sigmaAT^(4)=sigma.1.(T_(0)+10)^(4)=sigma.T_(0)^(4)(1+(10)/(T_(0)))^(4)[T_(0)=300K`given]
Using binomial theorem, `P_("rad")=sigma.(300)^(4).(1+(40)/(300))~~460xx(17)/(15)~~520J`
`P_("net")=520-460~~60WrArr` Energy radiated in 1 s = 60 J
(B) `P=sigmaA(T^(4)-T_(0)^(4))`
`dp=sigmaA(0-4T_(0)^(3).dT)anddT=-DeltaT_(0)rArrdp=4sigmaAT_(0)^(3)DeltaT_(0)`
(D) If surface area decreases, then energy radiation also decreases.
NOTE While giving answer (B) and (C) it is assumed that energy radiated refers the net radiation. If energy radiated is taken as only emission, then (B) and (C) will not be included in answer.