Change the chapter
The “steam” above a freshly made cup of instant coffee is really water vapor droplets condensing after evaporating from the hot coffee. What is the final temperature of 250 g of hot coffee initially at $90.0^\circ\textrm{C}$ if 2.00 g evaporates from it? The coffee is in a Styrofoam cup, so other methods of heat transfer can be neglected.
Question by OpenStax is licensed under CC BY 4.0.


Solution Video

OpenStax College Physics Solution, Chapter 14, Problem 47 (Problems & Exercises) (2:49)

Sign up to view this solution video!


2 votes with an average rating of 5.

Quiz Mode

Why is this button here? Quiz Mode is a chance to try solving the problem first on your own before viewing the solution. One of the following will probably happen:

  1. You get the answer. Congratulations! It feels good! There might still be more to learn, and you might enjoy comparing your problem solving approach to the best practices demonstrated in the solution video.
  2. You don't get the answer. This is OK! In fact it's awesome, despite the difficult feelings you might have about it. When you don't get the answer, your mind is ready for learning. Think about how much you really want the solution! Your mind will gobble it up when it sees it. Attempting the problem is like trying to assemble the pieces of a puzzle. If you don't get the answer, the gaps in the puzzle are questions that are ready and searching to be filled. This is an active process, where your mind is turned on - learning will happen!
If you wish to show the answer immediately without having to click "Reveal Answer", you may . Quiz Mode is disabled by default, but you can check the Enable Quiz Mode checkbox when editing your profile to re-enable it any time you want. College Physics Answers cares a lot about academic integrity. Quiz Mode is encouragement to use the solutions in a way that is most beneficial for your learning.

Calculator Screenshots

OpenStax College Physics, Chapter 14, Problem 47 (PE) calculator screenshot 1
Video Transcript
This is College Physics Answers with Shaun Dychko. We have some coffee in an insulated cup which means the only way that heat is going to leave is through this phase change of some of the coffee that is evaporating. So, there is a total of 250 grams to start with and 2 grams of that will evaporate leaving 248 grams left behind which we'll call m subscript w for water because the coffee is going to have the properties of water, the same specific heat of water 4186 joules per kilogram per Celsius degree and the latent heat of vaporization for this coffee that is evaporating is 2256 joules per kilogram and this number is not precisely true because that's true only when the water is at 100 degree Celsius but 90 degree Celsius is pretty close to that and so we will take that to be the latent heat of vaporization. So, the initial temperature is 90 degrees and we are asked to figure out what will the final temperature of the coffee be, after 2 grams of it, evaporates. So, there's going to be a amount of heat that is lost and that’s why the negative sign is there because it’s a loss in thermal energy equal to the mass of coffee remaining times it specific heat times the final temperature minus the initial temperature and that heat loss is going to be the heat gained by the vapour that is evaporating so the mass that’s evaporating times the latent heat of vaporization and then we are gonna solve this for T f coz we want to know what the final temperature of the coffee is. So we multiply through by m w C w and then we have positive m w C w T initial minus m w C w times T final and then we will take this term to the left side and then this term to the right side and then switch the sides around so that we have the unknown terms in the left and we are dividing both sides by m w C w and that isolates T f. So T final is mass of the water remaining times its specific heat times initial temperature minus the mass of the vapour that evaporates times the latent heat of vaporization divided by the mass of the water times specific heat of water. So that’s 248 times 10 to the minus 3 kilograms so that’s 248 grams converted to kilograms times specific heat of water times initial temperature of 90 degrees Celsius minus the 2 grams that evaporates written in kilograms times 2256 times 10 to the 3 joules per kilogram divided by 248 grams times specific heat of water and this gives a final temperature of 85.7 degree Celsius.