Home made ice cream demonstrates a technique for achieving sub-freezing temperatures. We can explain this anti-intuitive phenomena by using concepts we have already learned. We will make ice cream, invite another class to join us and have a little drama about heat exchange.
We will explore the way in which salt water can enable us to achieve a sub-freezing temperature using only ice. We hope to dramatize this amazing phenomena. We will have some fun.
Introduce the idea of the ice cream freezer and the fact that it can cool the ice cream mixture to sub freezing temperature. Begin making the ice cream. The class should have about one ice cream freezer for each eight people in the class.
Refer to the equation used in the last session:
Salt water has a lower freezing temperature than water. In fact, with the proper amount of salt, the freezing point of brine is -21.1°C. However, brine also "encourages" the ice to melt. The ice still must obey the equation above and absorb "heat" from the brine in order to melt. So, the brine gives up more heat and becomes colder. It can continue to give heat to the melting ice until the ice is gone or the brine cools to -21.1°C.
Step 1. The brine gives heat to the ice. The ice melts. The brine cools. It cools below the freezing point of pure water.
Step 2. The brine absorbs heat from the ice cream mixture and brings the mixture below its freezing temperature. The brine warms. So we have a cycle where the brine transfers heat from the ice cream in the container to the ice outside the container. The magic is that the brine and the ice cream can be below the freezing temperature of water and, more importantly, below the freezing temperature of the ice cream mixture.
When the visiting class arrives about halfway though the class period, they should be given ice cream and the instructor should explain the drama to them. Then, begin the drama, described below, with great good spirits and have some fun.
Hopefully, this can all be done in the remaining time. If the drama ends too quickly, eat some more ice cream. If it runs to long, just dismiss. The point should be perfectly clear.
We need lots of students for this drama both to eat the ice cream and to participate in the drama itself. So we expect that most physics classes will have to invite another class, not necessarily a science class, to participate. We will need a fairly large room or maybe the hall as a space for the drama to unfold. I can image that ice cream will be spilled so don't use a place that is difficult to clean.
In this drama we will re-enact the ice cream making sequence. The physics class will dramatize tiny particles of ice that melt and become water. They will also dramatize the sub-freezing water as it transfers heat.
The visiting class will dramatize tiny particles of the ice cream mixture as they cool and become ice cream
We will use Monopoly money to represent both heat and temperature in the drama. For the sake of concreteness, we will assume that the temperature is in Fahrenheit.
In order that the number of water people is about half of the original ice people, the heat or Monopoly money has to be distributed properly. Use the following formula to decide how much money to give to the ice cream people.
This does not have to be exact. The nearest $5 is fine. If the number of ice cream people is about the same as the number of ice people, the ice cream people should get about $70 each. The next paragraph assumes equal sizes.
The folks representing the ice cream mix will all be given $70 to represent 70°F and to represent 70 units of heat in some arbitrary heat unit. The ice cream folks are to mill around in a tight group representing the liquid phase of the ice cream mix. If there are singers in the group, they should lead a quick paced fun song.
The physics class will join together, locked arm in arm, in several rows. For real drama, they all need to slowly step to the right and left in a very cold dance. They have no money. However, to be freed of their lock-step dance, they need to receive $80. If there are singers in the group, they should sing "Song of the Volga Boatmen".
A solitary person will initially represent the brine. This person will have $32. Their goal is to free one of the ice people. They will do that by asking one of the ice cream people for some money. The ice cream person should be more than willing to give them money but they can never allow the wealth of the water person to exceed their own wealth. In the first transaction, the water person with $32 asks the ice cream person with $70 for money. The ice cream can provide only $19 because then the water will have $51 and the ice cream will have $51. The act of balancing the wealth between the water and the ice cream represents the fact that when two liquids are brought into contact they find an equilibrium temperature. That is, after mixing, they both have the same temperature.
The instructors will act as bankers. Their primary task will be to keep the ice cream folks in change so the ice cream folks can give the proper amount of money to the water folks.
The water should then give all his money to one of the ice people. (To be accurate, the water should give all but $2 but that is so close to zero that we will ignore the difference.) Then the water should immediately run back to the ice cream and ask for more money. This time, if they ask someone with $70, they should receive $35. They can, if they choose ask another $70 ice cream person for money and get $18 more. Then the water should run back and give $29 to the same ice person. If the water person has money left over, give it to a second ice person. In this case there will be $24 left over. Continue this operatation trying to free more of the ice people from their frozen state.
When the ice person receives $80, they magically change to a water person. They should give $50 to the banker (one of the instructors) and then immediately go to the ice cream, ask for money and deliver the money to the ice people as described above. Or they can go to the ice and give their remaining $30 away.
Of course, the bankers must assume this second task of receiving money from the former ice person. The act of receiving this money is much like the physical situation. The heat is absorbed by the ice so it may melt but its temperature does not rise. It stays near the freezing point of water. Hence, the heat, like the money, is out of circulation.
As time goes on, more ice people will turn into water people and they, in turn, will move money from the ice cream people to the ice people.
All the time the ice cream people are giving money away, they should also try to keep their individual wealth about the same. So if one has more than most, he should give some of his wealth to a poorer ice cream person. Whenever an ice cream person falls below $28 they must stop moving. They can still conduct money transactions but they can no longer move. If they are near another who is also below $28 they should link arms. Arm linking represents the freezing of the ice cream and its resistance to motion. If the ice cream people are equalizing their wealth, they should all freeze about the same time.
This recipe is from Eagle Brand®.
Class time required for making the ice cream mixture can be eliminated if the instructor (or aide) makes the mixture the night before class. Of course, the students will miss the fun of mixing.
If the ice cream mixture is well chilled prior to churning, one can reduce the churning time. A refrigerator will generally cool to only about 40°F. So, if one puts the container of the ice cream maker into an ice chest filled with ice, it will cool to 32°F. Do not submerge the container too far into the ice. That might allow water to leak into the container and ruin the ice cream mix.
Please test this operation. We hope that the ice cream will solidify within 20 to 30 minutes. If it does not, the instructor should make some provision to get the ice cream made so that it finishes at the proper time.
I am stealing the following excellent explaination of the cooling effect of salt in an ice and water mixture. We will not use it in class at this point because it talks of molecules, disolving of salt, etc. in a way that we have not yet examined. However, we can use this when we get further along. Here is the link to the original article. If the link goes bad, we still have the text.
Under normal conditions, ordinary water freezes at 0°C, or 32°F. However, if you add salt to water, its freezing point becomes lower. Let's look at why a salt water solution has a freezing point below zero, and how you can use this fact to make ice cream!
At the right is a container of water with several ice cubes in it (we'll just show one ice cube for simplicity). We've started with cold tap water at 10°C (about 50°F) and ice at 0°C, and we've placed the mixture in a nice, insulated cup that prevents the flow of heat into the cup from the outside world. Water molecules are constantly escaping from the solid ice into the liquid water (melting). At the same time, water molecules are being captured on the surface of the ice (freezing). But because the water molecules in the liquid are moving quickly (they are at elevated temperature compared to the ice), they can't easily be captured by the surface of the ice, so not very many of them freeze. Freezing occurs at a slower rate than melting. Because there are fewer water molecules being captured by the ice (being frozen) than there are ice molecules turning to water, the net result is that the amount of water increases, and the amount of ice decreases. Now as the ice melts, what happens to the temperature of the water? Of course, the water temperature falls because we've put a "cold thing" into the "warm water". But much more importantly, the water temperature falls because energy is removed from the water to melt some of the ice. In fact, if we start with enough ice in the container, eventually the water in the container will reach 0°C, along with the remaining ice. The "phase transition" from a solid to a liquid extracts energy from the liquid.
In the picture at the right, the water in the container has finally reached 0°C along with the remaining ice. Molecules of water are still escaping from the solid ice into the liquid water (melting), and molecules of water in the liquid are still being captured on the surface of the ice (freezing). But now, the rate of freezing is the same as the rate of melting, and the amount of ice and the amount of water won't change. The ice and water are said to be in dynamic equilibrium with each other. The ice is melting, and the water is freezing, but both are occurring at the same rate, so there is no net change in either quantity. Freezing occurs at the same rate as melting. This balance will be maintained as long as the container stays insulated or unless something else happens to favor one of the processes over the other.
What we've learned so far is that when an ice cube is immersed in water, some of the ice is always melting, and some of the water is always freezing. If these are both happening at the same rate, the contents of the container are at the freezing/melting point. For pure water, this happens at 0°C.
So how does adding salt to the water affect the result? Let's look. Here's the same container with the water at 0°C, only this time the water contains salt molecules. Adding salt, or anything other than water, disrupts the equilibrium. The salt molecules dissolve in the water, but do not attach easily to the solid ice. There are fewer water molecules in the liquid because some of the water has been replaced by salt. This means that the number of water molecules able to be captured by the ice (frozen) goes down, so the rate of freezing goes down. The rate of melting of the ice is unchanged by the presence of the salt, so melting is now occurring faster than freezing
But just as in the first picture, as ice melts, energy is extracted from the surrounding liquid, and the liquid cools. And it continues to cool until the system returns to equilibrium, where the number of molecules of water that are freezing is equal to the number of ice molecules that are melting. Eventually, the temperature falls sufficiently to make the water molecules slow down enough so that more can attach themselves to the ice. When the number of water molecules that are freezing equals the number of ice molecules that are melting, equilibrium will be reached again. In our example, this point is reached at -4°C, which would be the new freezing/melting point. The higher the concentration of salt, the lower the temperature of the new freezing/melting point.
Summary:
As ice begins to freeze out of the salt water, the fraction of water in the solution becomes even lower, and the freezing point drops further! However, this doesn't continue indefinitely. At some point the solution will become saturated with salt. This happens for salt in water at -21.1°C, which therefore is the coldest a saturated solution of salt and water can get. At that temperature, the salt begins to crystallize out of solution, along with the ice, until the solution completely freezes. The frozen solution is a mixture of separate salt (NaCl·2H2O) crystals and ice crystals. This heterogeneous mixture is called a eutectic mixture. Any foreign substance added to the water will cause a freezing point drop. For every mole of foreign particles dissolved in a kilogram of water, the freezing point goes down by roughly 1.8°C. Sugar, alcohol, or any chemical salt will also lower the freezing point and melt ice. Salt is used on roads and walkways because it is inexpensive and readily available. You might suppose that larger molecules might inhibit the freezing of water molecules even more, and have a more dramatic effect on the freezing point. However, that isn't the case. Actual molecules are so tiny compared to the distance they move through the liquid that size is hardly a factor at all.