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We decided to make an iced latte by adding ice to a 200 mL hot latte at 45 °C. The ice starts out at 0 C. How much ice do we need to add for the final drink to be 10 C? The latent heat of fusion of ice is 335 J/g. Approximate the latte as water. Express your answer in g, without specifying the units.

Respuesta :

Answer:

m = 77.75 g

Explanation:

Here we know that at equilibrium the temperature of the system will be 10 degree C

so heat given by hot latte = heat absorbed by the ice

now we have

heat given by latte = [tex]m s\Delta T[/tex]

[tex]Q_1 = (200)(4.186)(45 - 10)[/tex]

[tex]Q_1 = 29302 J[/tex]

now heat absorbed by ice is given as

[tex]Q_2 = mL + ms\Delta T[/tex]

[tex]Q_2 = m(335 + 4.186(10 - 0))[/tex]

[tex]Q_2 = m(376.86)[/tex]

now by heat balance we have

[tex]Q_1 = Q_2[/tex]

[tex]29302 = m(376.86)[/tex]

[tex]m = 77.75 g[/tex]

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