A sphere of ice at $0^o C$ having initial radius $R$ is placed in an environment having ambient temperature $> 0^o C$. The ice melts uniformly, such that shape remains spherical. After a time $‘t’$ the radius of the sphere has reduced to$r$. Assuming the rate of heat absorption is proportional to the surface area of the sphere at any moment, which graph best depicts $r (t)$.
- A
- B
- C
- D
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[$A$] 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.
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