Latent Heat and phase changes (difficult)

AI Thread Summary
To find the final temperature when 10g of ice at 0°C is mixed with 2g of steam at 100°C, the problem requires applying the first law of thermodynamics and considering latent heat. The initial approach involved setting the heat gained by the ice equal to the heat lost by the steam, but the calculations were incorrect. The correct method involves two steps: first, calculating the temperature when the steam's latent heat melts the ice, and then using a mass-weighted average to find the final temperature of the resulting water. The accurate final temperature is determined to be 40.4°C, confirming the provided answer.
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Homework Statement



10g of ice at 0 degrees Celcius is combined with 2 g of steam at 100 degrees Celcius. Find the final temperature of the resulting water.

Homework Equations



mc(Tf- Ti)
m(Lf) or m (Li)

The Attempt at a Solution



ΔQice=mLice+mcwaterTf
ΔQsteam=mLsteam+mcsteamTf-100 degrees celcius

I set this equations to 0 and solve for Tf and i get this

Tf=mCsTi+mLv-mLf/mCw+mCs and i get 93.9 degrees celcius and that is not the answer

the answer is 40.4 degrees celcius. help?
 
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Hint:

Solve the problem in two parts.

1. Use first law of thermo to determine water temperature when steam's latent energy melts ice.
2. Use mass weighted average to determine final temperature of mixture of two water solutions.

The answer provided is correct.
 
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