In this problem you will consider the balance of thermal energy radiated and absorbed by a person.Assume that the person is wearing only a skimpy bathing suit of negligible area. As a rough approximation, the area of a human body may be considered to be that of the sides of a cylinder of length L=2.0m and circumference C=0.8m.For the Stefan-Boltzmann constant use σ=5.67×10−8W/m2/K4.Part aIf the surface temperature of the skin is taken to be Tbody=30∘C, how much thermal power Prb does the body described in the introduction radiate?Take the emissivity to be e=0.6.Express the power radiated into the room by the body numerically, rounded to the nearest 10 W.part bFind Pnet, the net power radiated by the person when in a room with temperature Troom=20∘C

Respuesta :

Answer:

The thermal power emitted by the body is [tex]P_t = 286.8 \ Wm^{-2}[/tex]

The net power radiated is  [tex]P_{net} = 460 \ W[/tex]

Explanation:

From the question we are told that

   The length of the assumed hum[tex]T_{room} = 20 ^oC[/tex]an body is  L =  2.0 m

   The circumference of the assumed human body is  [tex]C = 0.8 \ m[/tex]

   The  Stefan-Boltzmann constant is  [tex]\sigma = 5.67 * 10^{-8 } \ W\cdot m^{-2} \cdot K^{-4}.[/tex]

    The temperature of skin [tex]T_{body} = 30^oC[/tex]

     The temperature of the room is  

    The emissivity is  e=0.6

The thermal power radiated by the body is mathematically represented as

           [tex]P_t = e * \sigma * T_{body}^4[/tex]

substituting value

        [tex]P_t = 0.6 * 5.67*10^{-8} * (303)^4[/tex]

        [tex]P_t = 286.8 \ Wm^{-2}[/tex]

The net power radiated by the body is mathematically evaluated as

    [tex]P_{net} = P_t * A[/tex]

Where A is the surface area of the body which is mathematically evaluated as

     [tex]A = C* L[/tex]

substituting values

      [tex]A = 0.8 * 2[/tex]

      [tex]A = 1.6 m^2[/tex]

=>    [tex]P_{net} = 286.8 * 1.6[/tex]

=>   [tex]P_{net} = 460 \ W[/tex]