For my daughter's science experiment, she placed six beverages (cola, diet cola, milk, chocolate milk, apple juice, and water) in the exact same amount in the exact same type and size of plastic cups, and placed all of the cups in a refrigerator at the same time and allowed them to remain in the refrigerator for the same period of time (4 hours). When the beverages were taken out and set on the same counter, in a room at approx. 70 degrees, a cooking thermometer was then used to measure the temperature of each of the beverages at different time intervals (the intervals were the same for all beverages)—i.e., the temperature of each was measured at 15 minutes, 45 minutes, 1 hour, and 90 minutes. The results were that all but two of the beverages held the same temperatures throughout the measuring period. The two beverages with different (colder) temperatures were diet cola and (white) milk. Of course, my daughter is supposed to cite to references that support (and explain) the basis of the test results/conclusions, and we are finding nothing that addresses this. "Viscosity" is the closest principal that we have found, but we cannot find anything that provides the viscosity levels for the separate beverages (hence, no conclusion can be drawn). Any ideas on where to find research references related to this? thanks,
[Physics] Why do some beverages stay cold longer than others
thermodynamicsviscosity
Related Solutions
The two "no" answers you've already received are correct for all practical purposes.
In real-world cases there can be a difference though. The difference depends on when the refrigerator decides to cycle on and cool. If the fridge cycles on a timer or based on heat energy then there will be a difference due to the added heat capacity. The outside of the refrigerator will acquire heat due to conduction, convection, and radiation from external sources.
All heat transfer depends on $\Delta T$. The greater the difference in temperature between two systems the faster heat will flow. When you add heat energy to a full refrigerator, the system has greater heat capacity so the temperature changes more slowly and $\Delta T$ is greater than it would be in an empty refrigerator. If the refrigerator could keep the temperature absolutely constant at all times the difference would not matter. Because a real system cools and then stops cooling in discrete steps, a loaded refrigerator acquires heat from the environment slightly faster because it stays colder for longer.
The difference is so small though that I'm sure it couldn't be measured.
But, if the refrigerator only cycles on at a specific temperature there will be no difference. I wrote a numerical simulation to test this. Here is the plot:
The simulation is a simplified, idealized, purely numerical one, hence the lack of units. The Y axis is temperature and the X axis is time. The red curve is the loaded refrigerator and green curve is the unloaded one. For the simulation I made the loaded fridge have double the heat capacity.
Assuming the refrigerator only cycles on when the temp reaches the top of the graph then there is no difference between the two. Although twice as much heat energy must be put into the loaded refrigerator, the simulation shows that it takes exactly twice as long. That is, the average rate of heat flow is identical.
So, the answer to the question depends on how the refrigerator works.
If the refrigerator is time interval or heat energy interval based, a loaded fridge takes more energy to maintain a cold temperature.
If the fridge is purely thermostat based, there is no difference in energy consumption.
Dirt is an exceptionally good insulator. As seasons change, the temperature of dirt 5-10ft underground changes a lot less than the temperature of the air. The deeper you go, the less the change. So, in the summer a basement will be "cool" because the ground surrounding it is cool (relative to outside temperatures), and in the winter it will be "warm" because the ground surrounding it is warm (relative to outside temperatures), despite "cool" and "warm" both being the same temperature (probably about 50-60F if you're in the southern USA).
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Best Answer
The specific heat of milk is considerably lower than that of water: http://www.engineeringtoolbox.com/specific-heat-fluids-d_151.html
So for a given amount of heat gained (through radiation and convection across the glasses surface) the temperature would increase more for milk than solutions that were more "water-like". But you saw that the temperature of milk was lower which suggests a different mechanism playing hte dominant role.
I would have thought that the ordering of solute concentration in these solutions to be chocolate milk > milk > cola > apple juice > diet cola > water. If anything I would have expect that a sugar rich solution would be less like water and so cola and apple juice have a different specific heat than water or diet cola. I would have guessed that evaporative losses would be greatest for the water-like solutions and would have expected chocolate milk, milk and regular cola to have less evaporative loss because solutes tend to attract water molecules and hold them in solution. So I would have guessed that the evaporative losses would be greatest for tap water and correspondingly less on the scale I outlined. None of that exactly fits your observation. I would suggest repeating the experiment with a longer time for equilibration at refrigerator temperatures and with the addition of glasses across which you place plastic wrap to prevent evaporative losses. This will be more "scientific" in that you will a) be repeating the experiment and b) be constructing a hypothesis to be tested.
The rate of loss of liquid and the amount of cooling that would cause will be directly related to vapor pressure of the liquids. Since the cooling of milk after its removal from the cow is done at least partly by evaporation, you should be able to search out data on that physical attribute. Likewise I suspect you can find out the concentration of sugar in cola and find citations for the effect of sugar on vapor pressure.