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You have a styrofoam container with 944 g of orange juice (specific heat of 3,770 J/(kg...

You have a styrofoam container with 944 g of orange juice (specific heat of 3,770 J/(kg · °C)) at 35.0° and you add a 73 g chunk of ice at 0°C. Assume the liquid and water mix uniformly as the ice melts and determine the final temperature of the mixture (in °C).
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Answer #1

Let the final temperature be T.

Heat gained by ice = Heat gained by ice at 0o C to become water at 00C + Heat gained by water to temperature T

= miC

where ci = sp. heat of water and L = latent heat of fusion of ice

=0,073( 334) + 0.073 × 4.187 × (T)

Heat lost by juice = mic;(35-T) 0.944 × 3.77(35-T)

where cj = sp. heat of juice = 3.77 kJ/kg0C

Now for equilibrium:

Heat gained by ice = Heat lost by juice

0,073( 334) + 0.073 × 4.187 × (T) = 0.944 imes 3.77(35-T)

24.382 +0.305T124.56 - 3.56T

(3.56 + 0.305)T- 124.56 - 24.382

T = 25.9 degree C

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