. A human body has a surface area of approximately 1 m^2
A human body has a surface area of approximately 1 m2. The normal body temperature is 10K above the surrounding room temperature T0. Take the room temperature to be T0 = 300 K. For T0 = 300 K, the value of (where σ is the Stefan Boltzmann constant). Which of the following options is/are correct?
A. Reducing the exposed surface are of the body (e.g. by curling up) allows humans to maintain the same body temperature while reducing the energy lost by radiation
B. If the body temperature rises significantly then the peak in the spectrum of electromagnetic radiation emitted by the body would shift to longer wavelengths
C. The amount of energy radiated by the body in 1 second is close to 60 Joules.
D. If the surrounding temperature reduces by a small amount ∆T0 << T0, then to maintain the same body temperature the same (living) human being needs to radiate ∆W = 4σT30 ∆T0 more energy per unit time
Correct Option is: (A), (C)
(A) Rate of energy loss due to radiation
dQ/dt = σAT4
Rate of energy adsorbed bdy surrounding
dQ/dt = σ eAT40
Net heat loss by radiation dQ/dt = σ eA (T4 – T40)
If exposed area A decreases. Rate of heat loss decreases.
If body temperature rises, spectrum of electromagnetic radiation shifts to smaller wavelength.
C. dQ/dt = σ eA (T4 – T40)
= σ eA [(T0 + ΔT)4 – T40]
= σ eAT40 [(1 + ΔT/T0 – 1]
= σ eAT40 [1 + 4ΔT/T0 – 1]
= σ eAT40 (4ΔT/T0)
= 1 × 460(4×10/300) = 184/3 = 61.3J