The normal body-temperature of a person is 97°F. Calculate the rate at which heat is flowing out of his body through the clothes assuming the following values. Room temperature = 47°F, surface of the body under clothes = 1.6 m2, conductivity of the cloth = 0.04 J s–1 m–1 °C–1, thickness of the cloth = 0.5 cm.
Given:
Body Temperature : T1 = 97 °F = 36.1 °C
Room temperature: T2 = 47°F = 8.3 °C
Surface area under clothes : A = 1.6 m2
Thermal conductivity of the cloth : K =0.04 J s–1 m–1 °C–1
Thickness of the cloth : x = 0.5 cm = 0.005 m
Formula used:
Rate of amount of heat flowing is given as:
Here, Δθ is the amount of heat transferred, ΔT is the temperature difference, K is the thermal conductivity of the material, A is the area of cross section of the material and x is the thickness of the material.
Here, ΔT = T1-T2 = 36.1-8.3 = 27.8 °C
Substituting we get,
Hence, the rate at which heat is flowing out of his body through the clothes is 355.84 J/s.