JEE Advanced 2017 · Paper 1 · Physics Q4

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PhysicsMultiple correct+4 / -2Question 4 of 54

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

The amount of energy radiated by the body in 1 second is close to 60 Joules

If the surrounding temperature reduces by a small amount

\Delta T_0 \ll T_0

, then to maintain the same body temperature the same (living) human being needs to radiate

\Delta W = 4\sigma T_0^3\Delta T_0

more energy per unit time

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

If the body temperature rises significantly then the peak in the spectrum of electromagnetic radiation emitted by the body would shift to longer wavelengths

Answer and worked solution

Official answer: C

Body temperature. $T=310$ K.

(A) The body radiates $\sigma T^4A=460\times(310/300)^4\approx525$ J each second. About 60 J is only the net loss, $\sigma A(T^4-T_0^4)$ . False.
(B) The body's own emission $\sigma T^4A$ does not change when the room cools. What changes is how much it absorbs: the net loss rises by $4\sigma T_0^3\Delta T_0$ . It does not radiate more. False.
(C) Emission is proportional to the exposed area, so curling up reduces the loss. True.
(D) By Wien's law $\lambda_m\propto1/T$ , the peak shifts to shorter wavelengths. False.

(C)

Topics:Radiation and Stefan's law Wien's displacement law

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JEE Advanced 2017 · Paper 1, Physics question 4