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**1. You have a tub of water that you are placing ice into. There is 300kg of water at 70 degrees celsius. You add 10kg of ice at -3 degrees C. What is the final temperature of the water? The latent heat of fusion for water is 33.5 x 10^4 j/kg**

I have worked out the best I can the problem as I understand it and I come up with an answer that does not quite make sense

**2.**

Q= heat

Qgained = Qlost;

therefore

Qgained - Qlost = 0

Q= heat

Qgained = Qlost;

therefore

Qgained - Qlost = 0

**3. ice is gaining ...water is losing**

mc(changeintemp) + mLfusion - mc(ChangeinTemp) = 0

mc(start - final) + mLfusion - mc(start - final)=0

mc(-3 - final) + mLfusion - mc(70-final)=0

((10*4186(-3-final)) + 33.5x10^4) - (300*4186(70-final))=0

(41,860(-3-final) + 33.5 *10^4) - (1,255,800(70-final))=0

-125,580 - 41,860final +33.5*10^4 - (87,906,000 - 1,255,800final)=0

-125,580 - 41,860final + 335,000 - 87,906,000 + 1,255,800final = 0

-41,860final + 1,255,800final + 209,420 - 87,906,000= 0

-41,860final + 1,255,800final -87,696,580 = 0

-41,860final + 1,255,800final = 87,696,580

final(-41,860 + 1,255,800) = 87,696,580

final(1,213,940) = 87,696,580

final = 87,696,580 / 1,213,940 = 72.241 degrees C??

if the -41,860 was positive it came to a plausable answer. Now, I've checked over and and over and I don't understand where my error is but... 87,696,580/ (41,860 + 1,255,800) = 67.5 degrees C. Is one of my signs backwards or did i setup the problem incorrectly. Thanks for any help.

mc(changeintemp) + mLfusion - mc(ChangeinTemp) = 0

mc(start - final) + mLfusion - mc(start - final)=0

mc(-3 - final) + mLfusion - mc(70-final)=0

((10*4186(-3-final)) + 33.5x10^4) - (300*4186(70-final))=0

(41,860(-3-final) + 33.5 *10^4) - (1,255,800(70-final))=0

-125,580 - 41,860final +33.5*10^4 - (87,906,000 - 1,255,800final)=0

-125,580 - 41,860final + 335,000 - 87,906,000 + 1,255,800final = 0

-41,860final + 1,255,800final + 209,420 - 87,906,000= 0

-41,860final + 1,255,800final -87,696,580 = 0

-41,860final + 1,255,800final = 87,696,580

final(-41,860 + 1,255,800) = 87,696,580

final(1,213,940) = 87,696,580

final = 87,696,580 / 1,213,940 = 72.241 degrees C??

if the -41,860 was positive it came to a plausable answer. Now, I've checked over and and over and I don't understand where my error is but... 87,696,580/ (41,860 + 1,255,800) = 67.5 degrees C. Is one of my signs backwards or did i setup the problem incorrectly. Thanks for any help.

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