• Entropy
• Heat
• Heat capacity
• Enthalpy of fusion (Latent heat)
• Thermal equilibrium

Estimated Time: 45 minutes

Students will set up a styrofoam cup with ice and water in it. As it reaches equilibrium, the students will calculate the final temperature and mass of ice to compare to the value measured at the end.

• An understanding of the first and second thermodynamic laws.
• Experience using the second law to calculate changes in entropy.
• Familiarity with the enthalpy of fusion.

• Tabletop Whiteboard with markers
• Thermometer
• Styrofoam cups
• Water at temperature varying from near freezing to near boiling
• Ice
• Balance for measuring mass
• A handout for each student
• Appropriately sized containers for transporting water

Before beginning the activity, briefly read over the instructions for the lab with the entire class so that students can answer any clarifying questions before beginning. Then, place the students into small groups and assign each group an initial temperature water to place in a styrofoam cup with ice. Remind them to begin answering the questions as their thermal system reaches equilibrium.

For this lab, it's very important to get students started quickly on placing their water and ice together so they can begin the process of reaching thermal equilibrium. Be sure that each group has insulated their system to their best ability (i.e. the styrofoam cup has a lid on it, place the styrofoam cup inside another cup for additional insulation, etc.).

Many groups find the mathematics of this activity–which is most of the work–surprisingly challenging. Some of the roadblocks will be:

• Many groups fail to recognize that the energy the water lost by heating the ice must have been gained by the ice. This (together with the heat capacity $C_p$ and the enthalpy of fusion) is the only physics needed before math can be applied to the problem.

• For groups that have warm enough water to melt all the ice, the problem is more mathematically challenging, as the students then need to find the final temperature of the water. An easy mistake is to suppose the melted water remains at 0 Celcius, though this doesn't correspond to equilibrium. Even after recognizing that all the water ends up at the same temperature, many groups struggle to “name the thing they don't know” (the final temperature) and set up the appropriate equations.

• Students often incorrectly apply the First Law to this problem, and assume that the work done is zero. When pressed, students will acknowledge that the volume changes when ice turns to water, and therefore work must be done. This could be an opportunity to discuss (or preview) Legendre transforms, depending on if they have already been introduced.

Roughly 20 minutes after each group has poured their water sample into the cup of ice, have each group present their findings. The groups should state what the initial temperature of their water was, their theoretical calculations for how much ice would be left (if any) and what temperature the water would be if no ice were left, and the actual values for how much ice was left and what temperature the water would be if no ice were left.

Some of the groups did not have to calculate the change in entropy of the system after the ice completely melted. Calculating the change in entropy after the ice in the cup melts is more challenging than calculating the change in entropy while the temperature is constant. If time permits, have a group with no ice left discuss how they calculated the change in entropy after the ice completely melted.

Several groups will likely have theoretical values that are not very accurate despite having done the math correctly. Have a discussion about the non-ideal aspects of this experiment that one would need to compensate for to make the theoretical calculations more accurate.