Discussion Forum



1)

A human body has a surface area of approximately 1m2. The normal body temperature is 10K above the surrounding room temperature T0. Take the room temperature to be T0= 300K. For T0  =300K, the value of  $\sigma T_0^4=460 Wm^{-2}$   (where σ is the Stefan Boltzmann constant). Which of the following options 1s/are correct?


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 temeprature reduces by a small amount $\triangle T_{0}<<T_{0}$, then to maintain the same body temperature the same (living) human being needs to radiate $\triangle W=4\sigma T_0^3\triangle T_{0}$ more energy per uint 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 human to maintain the same body temperature while reducing the energy lost by radiation

Answer:

Option B,C,D OR D

Explanation:

Assumption e=1

                       [black body radiation]

 $P=\sigma A (T^{4}-T_{0}^{4})$

(c)           $P_{rad}=\sigma AT^{2}=\sigma .1. (T_{0}+10)^{4}$

       =   $\sigma T_0^4(1+\frac{10}{T_{0}})^{4}$

                            [T0  = 300 Kg given]

    = $\sigma .(300)^{4}(1+\frac{40}{300})=460\times\frac{17}{15}=520J$

     Pnet= 520-460=60W

$\Rightarrow$  energy radiated in 1 s=60J

(b)   P=  $\sigma A(T^{4}-T_0^4)$

$dP=\sigma  A (0-4T_0^3 dT)$

  and  $dT= -\triangle T$

 $\Rightarrow$   $dP=4\sigma A T_0^3\triangle T$

(d)   If the surface area decreases, then energy radiation also decreases

Note: While giving answers b and c it is assumed that energy radiated refers to the net radiation. If  energy radiated is taken as the only emission then b and c will not be included in the answer