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

Answer:

125.04181 W

Explanation:

$\sigma$ = Stefan-Boltzmann constant = $5.67\times 10^{-8}\ W/m^2K^4$

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

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

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