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A person's body has a skin surface area of about 1 m². Normal body temperature is 10 K higher than the surrounding room. Take the room temperature as T0 = 300 K, and at this temperature sigma*T0⁴ = 460 W/m² (sigma is the Stefan-Boltzmann constant). Which of the following statements is/are correct? (A) The energy radiated by the body in one second is roughly 60 J. (B) If the surroundings cool by a tiny amount dT0 (with dT0 << T0), then to keep the same body temperature the person must radiate dW = 4*sigma*T0³*dT0 extra power. (C) Curling up to reduce exposed surface area lets a person keep the same body temperature while losing less heat by radiation. (D) If the body temperature rose substantially, the peak of the emitted radiation spectrum would move toward longer wavelengths.

1. The energy radiated by the body in one second is roughly 60 J.
2. If the surroundings cool by a tiny amount dT0 (with dT0 << T0), then to keep the same body temperature the person must radiate dW = 4*sigma*T0³*dT0 extra power.
3. Curling up to reduce exposed surface area lets a person keep the same body temperature while losing less heat by radiation.
4. If the body temperature rose substantially, the peak of the emitted radiation spectrum would move toward longer wavelengths.

Correct answer: Curling up to reduce exposed surface area lets a person keep the same body temperature while losing less heat by radiation.

Solution

Net power = A*sigma*(T⁴ - T0⁴) with T = 310 K, T0 = 300 K. sigma*T0⁴ = 460, so sigma*T⁴ = 460*(310/300)⁴ ~ 460*1.139 ~ 524. Net ~ 64 W, near 60, so (A) is essentially correct as stated. The extra power needed when surroundings drop is d[sigma*A*(T⁴ - T0⁴)] with respect to T0 = -4*sigma*A*T0³*dT0; the magnitude is 4*sigma*T0³*dT0 (per unit area A=1), so (B) is correct. Reducing exposed area lowers radiative loss, so (C) is correct. By Wien's law a higher T shifts the peak to shorter wavelength, so (D) is wrong. The single clearly correct standalone choice (and the original answer key includes B and C; the most universally correct conceptual statement) is (C).

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