Question

A person with external body temperature 35°C is present in a room at temperature 25°C. Assuming the emissivity of the body of the person to be 0.5 and surface area of the body of the person as 2.0 m2, calculate the radiant power of the person.

Answer 1

Answer on Question # 57293 – Physics – Molecular Physics | Thermodynamics

A person with external body temperature $35{}^{\circ}\mathrm{C}$ is present in a room at temperature $25{}^{\circ}\mathrm{C}$. Assuming the emissivity of the body of the person to be 0,5 and surface area of the body of the person as $2,0\,\mathrm{m}^2$, calculate the radiant power of the person.

Solution:

The radiant power of the body can be found from the following equation:

$$P = A _ {y} \sigma \cdot \left(T _ {b} ^ {4} - T _ {r} ^ {4}\right) \cdot S = 0, 5 \cdot 5, 6 7 \cdot 1 0 ^ {- 8} \cdot \left(3 0 8, 1 5 ^ {4} - 2 9 8, 1 5 ^ {4}\right) \cdot 2 = 6 3, 2 [ W ],$$

where $A_y = 0,5$ is the emissivity of the person's body;

$$\sigma = 5, 6 7 \cdot 1 0 ^ {- 8} \left[ \frac {W}{m ^ {2} \cdot K ^ {4}} \right] \text{ is the Stefan-Boltzmann constant};$$ $$T _ {b} = 3 5 + 2 7 3, 1 5 = 3 0 8, 1 5 [ K ] \text{ is the absolute external temperature of the human's body};$$ $$T _ {r} = 2 5 + 2 7 3, 1 5 = 2 9 8, 1 5 [ K ] \text{ is the absolute temperature in the room};$$ $$S = 2 \left[ m ^ {2} \right] \text{ is the surface area of the body}.$$

Answer: 63,2 W.

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