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High-altitude mountain climbers do not eat snow, but always melt it first with a stove. To see why, calculate the energy absorbed from a climber's body under the following conditions. The specific heat of ice is 2100 J/kg?C?, the latent heat of fusion is 333 kJ/kg, the specific heat of water is4186 J/kg?C?.
a) Calculate the energy absorbed from a climber's body if he eats 0.90
kg of -15?C snow which his body warms to body temperature of 37?C.
b) Calculate the energy absorbed from a climber's body if he melts 0.90
kg of -15?C snow using a stove and drink the resulting 0.90kg of water at 2?C, which his body has to warm to 37?C.

Respuesta :

Answer:

a) [tex]Q=467443.8\ J[/tex]

b) [tex]Q_m=299700\ J[/tex]

c) [tex]Q_2=131859\ J[/tex]

Explanation:

Given:

  • specific heat of ice, [tex]c_i=2100\ J.kg^{-1}.^{\circ}C^{-1}[/tex]
  • latent heat of fusion of ice, [tex]L=333000\ J.kg^{-1}[/tex]
  • specific heat of water, [tex]c_w=4186\ J.kg^{-1}.^{\circ}C^{-1}[/tex]

(a)

  • mass of snow, [tex]m_s=0.9\ kg[/tex]
  • initial temperature of snow, [tex]T_{is}=-15^{\circ}C[/tex]
  • Final temperature of the consumed mass, [tex]T_f=37^{\circ}C[/tex]

Now the energy absorbed from the body after eating this snow:

[tex]Q=m_s.c_i.\Delta T_i+m_s.L+m_s.c_w.\Delta T_w[/tex]

[tex]Q=0.9\times 2100\times (0-(-15))+0.9\times 333000+0.9\times 4186\times (37-0)[/tex]

[tex]Q=467443.8\ J[/tex]

(b)

Energy absorbed from the body in melting the ice is the total latent heat:

[tex]Q_m=m_s.L[/tex]

[tex]Q_m=0.9\times 333000[/tex]

[tex]Q_m=299700\ J[/tex]

(c)

  • initial temperature of water, [tex]T_{iw}=2^{\circ}C[/tex]
  • final temperature of water, [tex]T_{iw}=37^{\circ}C[/tex]

Now, the amount of energy invested by body for the water at this condition:

[tex]Q_2=m_s.c_w.\Delta T_2[/tex]

[tex]Q_2=0.9\times 4186\times (37-2)[/tex]

[tex]Q_2=131859\ J[/tex]

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