Discussion Forum

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?

Answer:

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]

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

     P_net= 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