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Brewed coffee is often too hot to drink right away. You can cool it with an ice cube, but this dilutes it. Or you can buy a device that will cool your coffee without dilution - a 200 aluminum cylinder that you take from your freezer and place in a mug of hot coffee.

q)If the cylinder is cooled to -20C, a typical freezer temperature, and then dropped into a large cup of coffee (essentially water, with a mass of 500g ) at 85C, what is the final temperature of the coffee?answer in 2 sig figs and answer in Celsius.

Respuesta :

Answer:

[tex]T_f=57.21\ ^{\circ}C[/tex]

Explanation:

Given:

  • mass of aluminium, [tex]m_a=0.2\ kg[/tex]
  • initial temperature of the aluminium cylinder, [tex]T_{ia}=-20\ ^{\circ}C[/tex]
  • mass of coffee, [tex]m_c=0.5\ kg[/tex]
  • initial temperature of coffee, [tex]T_{ic}=85\ ^{\circ}C[/tex]
  • specific heat of coffee (assuming water), [tex]c_w=1000\ J.kg^{-1}.^{\circ}C^{-1}[/tex]
  • specific heat of aluminium, [tex]c_a=900\ J.kg^{-1}.^{\circ}C^{-1}[/tex]

When the coffee and the aluminium cylinder come in contact then heat released by the coffee is equal to the heat gained by the aluminium.

Mathematically:

[tex]Q_c=Q_a[/tex]

[tex]m_c.c_w. (T_{ic}-T_f)=m_a.c_a.(T_f-T_{ia})[/tex]

[tex]0.5\times 1000\times (85-T_f)=0.2\times 900\times (T_f-(-20))[/tex]

[tex]42500-500\times T_f=180\times T_f+3600[/tex]

[tex]T_f=57.21\ ^{\circ}C[/tex] is the final temperature of agreement.

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