Question

Assume that the total surface area of a human body is $1.6{\text{m}}^2$ and that it radiates like an ideal radiator. Calculate the amount of energy radiated per second by the body if the body temperature is ${37}^{\circ }\text{C}$.

Stefan constant $=6.0\times {10}^{-8}\text{W}{\text{m}}^{-2}{\text{K}}^{-4}$.

• A. $732\text{J}$
• B. $887\text{J}$
• C. $993\text{J}$
• D. $632\text{J}$

Answer 1

The correct option is B $887\text{J}$

Given that,
Area that radiates the energy, $A=1.6{\text{m}}^2$

Temperature, $T={37}^{\circ }\text{C}=273+37=310\text{K}$

For Ideal radiator, emissivity is $1$

According to the Stefan-Boltzman`s law,

The energy radiated per second by an ideal radiator is,

$E=\sigma A{T}^4$

$\Rightarrow E=6\times {10}^{-8}\times 1.6\times (310{)}^4$

$\Rightarrow E=887\text{J}$

Hence, option $\left(B\right)$ is correct.

Why this question? Concept: When the energy is dissipated through radiation, Stefan’s law is used to calculate the rate of energy dissipation and rate of energy absorption. According to this law, the rate of energy dissipation or absorption is directly proportional to the fourth power of the temperature.