What is the net power that a person with surface area of $1.20 \mathrm {~m} ^ { 2 }$ radiates if his emissivity is 0.895 , his skin temperature is $27 ^ { \circ } \mathrm { C }$ and he is in a room that is at a temperature of $17 ^ { \circ } \mathrm { C } ?$ $\left( \sigma = 5.67 \times 10 ^ { - 8 } \right.$ $\left. \mathrm { W } / \mathrm { m } ^ { 2 } \cdot \mathrm { K } ^ { 4 } \right)$

Question

What is the net power that a person with surface area of $1.20 \mathrm {~m} ^ { 2 }$ radiates if his emissivity is  0.895 , his skin temperature is $27 ^ { \circ } \mathrm { C }$ and he is in a room that is at a temperature of $17 ^ { \circ } \mathrm { C } ?$ $\left( \sigma = 5.67 \times 10 ^ { - 8 } \right.$ $\left. \mathrm { W } / \mathrm { m } ^ { 2 } \cdot \mathrm { K } ^ { 4 } \right)$

Quizplus · Accepted Answer

The net power radiated can be calculated using the Stefan-Boltzmann law: $ P = e \sigma A (T_{\text{skin}}^4 - T_{\text{room}}^4) $. Convert temperatures to Kelvin and substitute the values: $ e = 0.895 $, $ A = 1.20 \, \text{m}^2 $, $ T_{\text{skin}} = 300 \, \text{K} $, $ T_{\text{room}} = 290 \, \text{K} $, and $ \sigma = 5.67 \times 10^{-8} \, \text{W/m}^2 \cdot \text{K}^4 $. The calculation gives approximately 62.6 W.

What Is the Net Power That a Person with Surface 1.20 m21.20 \mathrm {~m} ^ { 2 }1.20 m2

What Is the Net Power That a Person with Surface $1.20 \mathrm {~m} ^ { 2 }$