Steam and ice interact, find final temperature

[mindarson]

Problem:

If 5.0 g of steam at 100 deg C interacts with 20 g of ice at 0 deg C, what is the final temperature of the resulting 25 g of water?

My thinking on the solution:

I figure I can use the equation

delta Q = mC(delta T)

to calculate the final temperature, where m = 25 g and C is specific heat of water.

I can find delta Q by calculating how much thermal energy the steam loses in condensing and subtract how much thermal energy the ice gains in melting, using the latent heats of vaporization and fusion respectively.

Am I on the right track here?

 

[gneill]

You're thinking along the right lines. In general you'll want to verify whether or not all of the ice can melt with the energy available, or if you'll end up with a mixture of some ice and some water. So compare the energy you'd get from condensing the steam and taking the resulting water to zero C with the energy required to melt all of the ice. If there's more than enough energy left over, then proceed as you've indicated.