Question

The basal metabolic rate is the rate at which energy is produced in the body when a person is at rest. A 66 kg (146 lb) person of height 1.83 m (6.0 ft) would have a body surface area of approximately 1.9 m2. What is the net amount of heat this person could radiate per second into a room at 18.0 ∘C (about 64.4 ∘F) if his skin's surface temperature is 31.0 ∘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.) Express your answer in watts.

answer is 147.59but i need help with the next part

Normally, 80 % of the energy produced by metabolism goes into heat, while the rest goes into things like pumping blood and repairing cells. Also normally, a person at rest can get rid of this excess heat just through radiation. Use your answer from Part A to find this person's basal metabolic rate.

Answer 1

given
m = 66 kg
A = 1.9 m^2
Th = 31 C = 31 + 273 = 304 K
Tc = 18 C = 18 + 273 = 291 K
emissivity, e = 1

According to Stefan-Boltzmaan's law,
power radiated by the person,

P = e*A*sigma*(Th^4 - Tc^4)

= 1*1.9*5.67*10^-8*(304^4 - 291^4)

= 147.6 W

from the given data

80% of person's basal metabolic rate = power radiated by the person

0.8*person's basal metabolic rate = 147.6

person's basal metabolic rate = 147.6/0.8

= 184.5 W <<<<<<<<<-------------Answer