Question

The basal metabolic rate is the rate at which energy is produced in the body when a person is at rest. A 71 kg ( 157 lb ) person of height 1.75 m (5.7 ft ) would have a body surface area of approximately 1.90 m².

What is the net amount of heat this person could radiate per second into a room at 19.0 °C (about 66.2 °F) if his skin's surface temperature is 30.0 °C? (At such temperatures, nearly all the heat is infrared radiation, for which the body's emissivity is 1.0, regardless of the amount of pigment.)

Answer 1

125.04181 W

Step-by-step explanation:

`\sigma` = Stefan-Boltzmann constant =
`5.67* 10^(-8)\ W/m^2K^4`

A = Surface area = 1.9 m²

`T_b` = Skin surface temperature = 19°C

`T_s` = Room temperature = 30°C

`\epsilon` = Emissivity = 1

Radiated thermal energy is given by

`P=\epsilon A\sigma (T_b^4-T_s^4)\\\Rightarrow P=1* 1.9* 5.67* 10^(-8)((273.15+30)^4-(273.15+19)^4)\\\Rightarrow P=125.04181\ W`

The net amount of heat this person could radiate per second into the room is 125.04181 W