C. Now, we'll flip this problem around. We would like to know how much of the drink must evaporate for it to reach exactly the preferred drinking temperature of 60 C. We want to solve for the final number particles Nf, or moles nf, remaining in the drink at exactly that temperature. 1. Write an expression for AU = Uf - Ui in terms of Ti, Tf, Ni, and Nf (or better moles, ni, and nf) [Hint: it is best to plug values a bit later in the process. Only write down the expression here.] 2. Just like before, write now an expression for the amount of energy carried away by the evaporating molecules (in terms of the heat of vaporization, N, and Nf). How does this energy relate to the change of energy AU of the remaining liquid? (Hint: pay special attention to the signs of each energy change). Use the two expressions for AU (with the correct signs) to find Nf at 60 C. 3. Determine the percent of the drink that was lost, Ni-Nf ni-nf Ni ni or -(they are the same). D. This method of cooling down a drink still involves waiting a while. If we're impatient, we could instead add a little tap water (say at 15 C). Find the volume of tap water necessary to cool the hot drink to 60 C, assuming no energy is lost to either evaporation or conduction.