A human body has a surface area of approximately $1 \mathrm{~m}^2$. The normal body temperature is $10 \mathrm{~K}$ above the surrounding room temperature $T_0$. Take the room temperature to be $T_0=300 \mathrm{~K}$. For $T_0=300 \mathrm{~K}$, and the value of $\sigma \mathrm{T}_0^4=460 \mathrm{Wm}^{-2}$ (where $\sigma$ is the Stefan-Boltzmann constant). Which of the following option is/are correct?
[$A$] The amount of energy radiated by the body in $1$ second is close to $60$ Joules.
[$B$] If the surrounding temperature reduces by a small amount $\Delta \mathrm{T}_0<<\mathrm{T}_0$, then to maintain the same body temperature the same (living) human being needs to radiate $\Delta \mathrm{W}=4 \sigma \mathrm{T}_0^3 \Delta \mathrm{T}_0$ more energy per unit time.
[$C$] 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.
[$D$] If the body temperature rises significantly then the peak in the spectrum of electromagnetic radiation emitted by the body would shift to longer wavelengths.
IIT 2017, Advanced
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- Heat radiated by body remains unchanged even after change in room temperature.
- Energy lost by the radiation depends upon the surface area.
- From Wien's law $\lambda_m T=$ constant
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