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Chapter 19: Q. 37 (page 544)

Radiation from the head is a major source of heat loss from the human body. Model a head as a 20-cm-diameter, 20-cm-tall cylinder with a flat top. If the body’s surface temperature is 35°C, what is the net rate of heat loss on a chilly 5°C day? All skin, regardless of color, is effectively black in the infrared where the radiation occurs, so use an emissivity of 0.95.

Short Answer

Expert verified

The accurate answer is 25.6 W.

Step by step solution

01

Given Information

Given:

Diameter of the head, d=20cm

Therefore, radius, r=10cm=0.1m

Height of the head, h=20cm=0.2m

Emissivity, e=0.95

Surface temperature of the body, T=35°C=(35+273)K=308K

Ambient temperature,

T0=5°C=(5+273)K=278K
02

Calculation

On the basis of temperature T0

P=eδA(T4-T04)

On the basis of provided information:

A=πDh+·πD2/4=πD(h+D2)

On the basis of substituting numerical case

P=eδπD(h+D4)(T4-T04)=0.95·5.67·10-8·π·0.2·(0.2+0.2/4)·(3084-2784)=25.6W

Therefore, the accurate answer is 25.6 W.

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