Calculating the final temperature of a mixture when ice & water

[Jham808]

Hello,

How do I calculate the following. The final temperature of a mixture of of ice and water. Where 176grams of ice at -10celsius mixes with 206 grams of water at 73.3celsius. I have tried this equation in multiple fashions and cannot seems to come to a consistent answer! Any help would be appreciated!

Why does the below not work?
water specific heat=4.184
ice specific heat= 2.11
heat of fusion=334

((specific Heat ice)X(Mass ice)x(∆temperature))+((mass ice)*(heat of fusion))+((specific Heat ice)X(Mass ice)x(x-0))=((specific Heat water)X(Mass water)x(∆temperature))

any help would be great appreciated

Additional Details
This is taking place in a completely insulated environment.

 

[voko]

Try doing this in stages. How much heat is required to bring the ice to the point of melting? Does the water have that much heat in it? If it does, then how much heat is left? Is it enough to melt all the ice? And so on.

 

[Jham808]

Hello Voko,

I have tried this in stages but continue to do something incorrectly.

The Amount of Energy in Water
((specific Heat water)X(Mass water)x(∆temperature))
4.18 X 73.3C X 206gram=63,117Joules

The Amount of Energy to get ice to melting point
((specific Heat ice)X(Mass ice)x(∆temperature))
2.11 * 10c * 176grams=3,713Joules

Energy for Melting
((mass ice)*(heat of fusion))
334*176=58,784

Total Energy of ice melt and bringing to melting point
((specific Heat ice)X(Mass ice)x(∆temperature))+((mass ice)*(heat of fusion))
62,497

62,497<63,117 complete melting of ice occurs

the remaining energy is 602 joules
the total remaining water mass is 176+206=382grams
620joules=382grams * 4.18 * (x-0)
602= 1,597 * (x-0)
0.38=(x-0)

This does not seem correct though

 

[voko]

I get 620 J for the residual heat.

 

[Jham808]

Sorry 620 is the number that I come to. "602" was a typo. Is this the correct calculation?

 

[voko]

Sorry 620 is the number that I come to. "602" was a typo. Is this the correct calculation?

I do not see any error.

 

[voko]

I do not see any error.

Actually, I do.

This: "176+206=326" can't be right.

 

[Jham808]

good catch I have corrected the 602 error and 326 error in my post. Other than those two Items, you believe my method is the exact way to calculate this problem?

 

[voko]

Everything else looks good.