## Phase Changes

Melting, freezing, boiling or evaporation and condensation (the reverse of evaporation) can be described in terms of heat transfer. These processes, in which one substance changes from a solid to a liquid, liquid to gas, etc., are called phase transitions. Ice, water and water vapor are said to be different phases of water. For interactions involving phase changes, the basic description in terms of heat transfer remains the same. The NET heat exchanged is zero. An alternate way of describing the interaction is that the heat lost by one part of the system equals that gained by the other. Phase transitions complicate the situations slightly. The following experiment and exercise illustrate the transfer of thermal energy when phase transitions are involved.

Notes:  0oC ice must come from a mixture of ice and water that has come into equilibrium.  There is a pan in the back of the lab.   Room Temperature water has been exposed to the room long enough to come to equilibrium with the room.  Again, there is a pan of Room Temperature water at the back of the lab.  It is nearly impossible to obtain Room Temperature water from the faucet!

### Experiment

• Acquire the data.
• Start Logger Pro™ by double clicking on the "Phase Change Lab" icon in the PHY 174 or PHY 184 folder.  Check the room temperature calibration of the Temperature Probe by comparing the value obtained using Logger Pro to that of the liquid-in-glass thermometer with the bulb near the tip of the Temperature Probe.  If there is a major discrepancy, tell your instructor.
• Measure the mass of an empty Styrofoam cup. Place 20g  (approximately 20 ml) of room temperature water in a Styrofoam cup.  Determine the mass of the water by measuring the mass of the cup plus water and subtracting off the mass of the empty cup.
• Determine the temperature of the water by collecting a set of data while stirring gently, and then use the Statistics option to find the best estimate of the starting temperature. Record this temperature along with its uncertainty.
• Dry some of the 0oC ice with paper towels. Place the 0oC ice in the cup. (Use a lot of ice -- about one or two times the volume of the water. )
• Stir continuously with a stirring rod, while measuring the temperature with the temperature sensor.
• Notice that the temperature is going down. When the temperature STOPS going down (at approximately 0oC ), immediately pour the water into a graduated cylinder, leaving the ice behind. It is convenient to use a funnel when pouring the water into the cylinder -- any ice that spills will be trapped in the funnel.
• Record the volume of water in the graduated cylinder and determine how much ice melted - remember, the density of water is 1 g/mL.
• Repeat the experiment with 40, 60, 80 and 100 g of room temperature water. Be sure there is always plenty of ice in the cup during the melting process.
• For each experiment, calculate the heat lost by the room temperature water (which is the heat gained by the ice).  This is just Q=mcDT.  The specific heat of water is 1 cal/(g oC).
• Calculate the mass of ice melted.  Since the density of water is 1 gram/ml, the mass is grams is the final volume minus the initial volume.
• Plot a graph of the heat gained by the ice versus the mass of ice melted using Graphical Analysis™ or Logger Pro.
• The graph should be approximately a straight line. Find the best-fit straight line and determine the slope of that line. What does the fact that the line is straight indicate? How do you interpret the slope?

The amount of heat required to melt one gram of ice is called the latent heat of fusion of ice. Careful measurements give 80 cal/g for the latent heat of ice. How does your result compare?

### Thought Experiment

The effect of heat transfer on objects undergoing a phase transition is different from its effect on objects undergoing a temperature change. Transfer of heat is still thought of as the cause of what happens, but the effect of the heat transfer is different than usually expected. Instead of raising the temperature of the ice, the heat melts the ice without changing its temperature. There is another difference as well, In interactions with no phase change, the heat received by the cold object is evenly distributed -- shared equally among all of the grams (mass) of the cold substance. In the case of melting, all of the heat goes to just the ice that melts. No heat goes to the unmelted ice.

The following exercise is a "thought experiment" that has you track how ice is melted by following quanta of heat. It might help to think of the ice in a plastic bag to keep it separate from the water in the container.  Equilibrium occurs when the temperatrue of the bag's contents matches the temperature of the surrounding water.

Exercise: A 25 g ice cube is put in 200 g of water at 20oC . What will be the final temperature? Reason out the solution instead of calculating it directly!

To do this, imagine sending heat from the hot material to the cold material in small amounts until equilibrium is reached. Since ice and water can only coexist in equilibrium at 0oC , all of the ice must be melted before the temperature of the cold material can be raised above 0oC. At the outset, it is not obvious whether all of the ice will melt. If re remove 80 cal of heat from water, the temperater of water will decrease according to Q=mcDT.  This amounts to a drop of 0.4 Co if the mass of the water is 200 grams.  Adding 80 cal of heat to ice at 0oC will melt one gram, leaving 24 grams remaining.   Continue until all of the ice has melted or the water has a temperature of zero Celsius.  If all of the ice melts and  the if the water temperature is not 0oC, keep transferring heat (possiblly smaller amounts) until the water from the melted ice has the same temperature as the originally 20oC water.

Keep track of your calculations by making a table like the following.

 Heat Transferred Temp of added water Mass of unmelted ice Mass of melted ice Temperature of melted water 0 cal 20oC 25 g 0 g 0oC 80 cal 19.60oC 24 g 1 g etc.

Continue the process until you reach equilibrium. What is the final temperature? If it is 0oC, how much ice remains?

Web Author: Barney Taylor, MUH