Question

The skin temperature of a person is 34o C and his body surface area is about 1.8 m2 . He is standing bare skin in a room where the air temperature is 24o C and the walls are 17o C. He is metabolizing food at a rate of 155 W, the emissivity of his skin is 0.97 and there is a 5mm thick dead layer (immobile) air next to his skin acting as an insulation. a./ at what rate his body is losing heat by conduction

Answer 1

the rate at which his body is losing heat by conduction is 93.6 J/s

Step-by-step explanation:

Given that;

surface area A = 1.8 m²

Skin temperature of the person Tp = 32°C = ( 34 + 273.15 ) = 307.15 K

Temperature of Air
`T_(air)` = 24°C = ( 24 + 273.15 ) = 297.15 K

Temperature of wall
`T_(wall)` = 17°C = ( 17 + 273.15 ) = 290.15 K

Length ( thick dead layer = 5 mm = 0.005 m

Skin emissivity = 0.97

Rate of metabolism = 155 W

rate his body is losing heat by conduction = ?

first we determine the difference in temperature between the skin and air

so

ΔT = 307.15 K - 297.15 K = 10 K

we know that; coefficient of thermal heat conductivity of air k = 0.026 W/mK

so

rate of heat loss by conduction Q/ΔT will be;

Q/ΔT = (KA/L)ΔT

so we substitute

= ( 0.026 × 1.8/ 0.005 )10

= 9.36 × 10

= 93.6 J/s

Therefore, the rate at which his body is losing heat by conduction is 93.6 J/s