100 g of ice at -5.0 C is added to 30 g of steam at 100 C. Find the final temperature of the resulting water.

Answer 1

Look up the latent heat of fusion (L_f) and the latent heat of vaporization (L_V) in J/g of water and the specific heats for w solid, liquid, and gas. The hard part about this problem is knowing in what phase that they end up. In order to solve this, you need to constantly check that the heat gained by the ice is lost by the steam as they approach the same state. You might just jump in and assume that they'll both end up as liquid water at the same final temperature. If it doesn't work, you'll have insight into how they end up.

Assuming they both end up as water:

m_Ic_I(0 - T_Ii) + m_IL_f + m_Ic_w(T_f - 0) = m_sc_s(T_si - 100) + m_sL_V + m_sc_w(100 - T_f) and solve for T_f

If it doesn't work, It may be that only some of the steam condenses because L_V is so large. In that case the last term would not be there and you would be solving for m in mL_V and T_f would be 100 degrees C.

Note that L's are often in kJ/g and c's in J/gC