Anonymous asked in 科學及數學其他 - 科學 · 6 years ago

Heat transfer

I want to ask a question about the thermodynamics.

Suppose you are sleeping in outer space and are radiating into vaccum. How thick should you sleeping bag be? The bag is made of material with thermal conductivity k=0.025J/msK, and the outer surface area is 2 m^2. Let the minimum rate of heat generated by your body be 97 Js^-1 and your body temperature by 310K.

Thank you~~

1 Answer

  • 天同
    Lv 7
    6 years ago
    Favorite Answer

    Let T be the temperature on the outer surface of the sleeping bag.

    Hence, by Stefan's Law on radiation,

    97 = (5.67 x 10^-8).(2).T^4

    where the constant (5.67 x 10^-8 w/m^2.K^4 ) is Stefan's constant

    i.e T = 171 K

    The heat radiated out from the surface of the sleeping bag comes from body heat which is conducted through the bag material.

    Hence, 97 = 0.025 x 2 x (310 - 171)/d

    where d is the thickness of the sleeping bag

    solve for d gives d = 0.0716 m = 7.2 cm

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