Latent Heat and phase changes (difficult)

[ScienceGeek24]

Homework Statement

10g of ice at 0 degrees celsius is combined with 2 g of steam at 100 degrees celsius. 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 celsius

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 celsius and that is not the answer

the answer is 40.4 degrees celsius. help?

 

[LawrenceC]

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.