Heat Radiation and Energy Loss from Human Body

To determine the correct option(s), let us analyze each statement individually using the principles of thermal radiation and thermodynamics:

1. Analysis of Option [A]

According to Stefan-Boltzmann Law, the total rate of energy emitted (radiated) by a body of surface area $A$ at absolute temperature $T$ is given by: $P_{\text{emitted}} = e \sigma A T^4$

Assuming the emissivity of human skin $e \approx 1$, surface area $A = 1\text{ m}^2$, room temperature $T_0 = 300\text{ K}$, and body temperature $T = T_0 + \Delta T = 310\text{ K}$ (where $\Delta T = 10\text{ K}$):

$P_{\text{emitted}} = \sigma A T_0^4 \left(1 + \frac{\Delta T}{T_0}\right)^4$

Using the binomial approximation $(1 + x)^n \approx 1 + nx$ for $x = \frac{10}{300} \ll 1$: $P_{\text{emitted}} \approx \sigma A T_0^4 \left(1 + 4\frac{\Delta T}{T_0}\right)$ $P_{\text{emitted}} \approx (460\text{ W m}^{-2}) \times (1\text{ m}^2) \times \left(1 + 4 \times \frac{10}{300}\right) = 460 \times \left(1 + \frac{2}{15}\right) \approx 521.3\text{ W}$

Thus, the energy radiated by the body in $1\text{ second}$ is approximately $521.3\text{ Joules}$.

(Note: The value $60\text{ Joules}$ actually corresponds to the net rate of heat loss $P_{\text{net}} = \sigma A (T^4 - T_0^4) \approx 4 \sigma A T_0^3 \Delta T \approx 61.3\text{ W}$, not the total energy radiated).

Therefore, Option [A] is incorrect.

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2. Analysis of Option [B]

The power radiated by the human body depends only on its own surface area, emissivity, and absolute body temperature $T$: $P_{\text{emitted}} = e \sigma A T^4$

If the surrounding room temperature drops by $\Delta T_0$, but the body temperature $T$ is kept constant, the rate at which the body emits radiation remains unchanged.

However, the power absorbed from the surroundings ($P_{\text{absorbed}} = e \sigma A T_0^4$) decreases, thereby increasing the net rate of heat loss. To maintain a constant body temperature, the human body needs to generate (produce via metabolism) extra energy per unit time, rather than radiate more energy.

Therefore, Option [B] is incorrect.

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3. Analysis of Option [C]

The net rate of heat loss by thermal radiation is given by: $P_{\text{net}} = e \sigma A (T^4 - T_0^4)$

Since $P_{\text{net}}$ is directly proportional to the exposed surface area $A$, reducing the effective surface area exposed to the environment (for example, by curling up into a ball) directly reduces $P_{\text{net}}$. This allows humans to conserve body heat and maintain temperature while minimizing radiative energy loss.

Therefore, Option [C] is correct.

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4. Analysis of Option [D]

According to Wien's Displacement Law, the peak wavelength $\lambda_{\text{max}}$ of the emitted radiation spectrum is inversely proportional to the absolute temperature $T$: $\lambda_{\text{max}} T = b \implies \lambda_{\text{max}} = \frac{b}{T}$

If the body temperature $T$ increases significantly, $\lambda_{\text{max}}$ decreases, which means the peak of the spectrum shifts to shorter wavelengths (higher frequencies), not longer wavelengths.

Therefore, Option [D] is incorrect.

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Conclusion

The correct option is [C].