52 States in 8 Months

Maybe you want a lot of ice. Maybe you want no ice.

Posted in University stuff by Ulf on May 6, 2009

Maybe you want a lot of ice. Maybe you want no ice. Maybe you want your top securely fastened, or maybe you want to go topless. Hmmm? Maybe you want to mix Coke and Sprite? Maybe you want to let your cup runneth over (we wish you wouldn’t). Whatever you do, make sure to have things your way.

This is what the Burger King soda cups say, and actually I chose to have a lot of ice. Enough ice in fact to do a little experiment.

A Pepsi bottle says that a serving of 240ml contains 28g sugar which accounts for 9% of my daily needs of carbohydrates. Wikipedia says that these 28g sugar contain about 106 to 109 kcal, while Pepsi says that there are only 100kcal in a 240ml serving. But in this experiment I didn’t care about energy at all, so this doesn’t matter.

I wanted to play around with the densities of different fluids and their effect on buoyancy. Everybody knows that the hardly preventable melting of the arctic ice will not raise the sea water level since the arctic ice swims, but the similarly unpreventable melting of the antarctic will. Ok, some of the ice on Antarctica is also floating, and there is so much ice that melting it will really take a long time. Now, I wanted to find out the effects of ice swimming not on fresh water, but on a water-based solution. Salt water for example, or sugar water. Since I wanted to drink the outcome of my experiment, I chose the sugar water.

So let’s start. I took two plastic cups, both 17.5g of weight. I added about 143g of ice each and then filled them up to the brim with water and Pepsi:

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As expected the Pepsi glass weights more since the sugar increases the fluid density. Let’s assume that I filled both cups to the same level and that there are no more hidden air bubbles inside. Then 152g of water have the same volume as 166g of Pepsi, resulting in a Pepsi density of roughly ϱPepsi=1090kg/m3. Please don’t give to much on this number, it’s not very accurate. All I want to say is that the density of Pepsi is higher than the density of tap water.

Well, since Pepsi has a higher density, a swimming cube of ice needs to displace less Pepsi than water for generating the same buoyancy force. Now, since the underwater volume of my ice cubes is smaller for the ice swimming in the Pepsi than for the ice swimming in the water, we can expect to have higher icebergs sticking out of the Pepsi cup. And indeed, the theory works:
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Now an interesting question comes up: Would the Titanic have seen the icebergs earlier if the ocean was made of Pepsi instead of seawater? You might argue that seawater is also just a solution of water and salt which renders seawater to be pretty much the same as Pepsi or Coke. However, the density of seawater is roughly ϱSeawater=1030kg/m3. That means that Pepsi has a much higher density than seawater and the Titanic might have made it! Congress, I recommend a law to fill the oceans with Pepsi or Coke, for safety reasons. Maybe Pepsi for the Pacific and Coca-Cola for the Atlantic?

My experiment however was about melting the ice, not ramming ships into it. Therefore I had to wait. The following pictures were taken 5, 10, 15, 32, 40, 71, 86 and 111 minutes after starting the experiment.

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About 140 minutes after the experiment started the last few ice cubes melted. I wanted to take a picture, but just in that moment something strange happened. All of the sudden most Pepsi evaporated!
bild8401I don’t know why the water stayed where it was.

Anyway, what have we learned from this experiment?

  1. Pepsi weights more than water.
  2. The water level in Pepsi doesn’t change at all when the ice melts.
  3. A cup full of ice and Pepsi needs about 2.5 hours to completely melt away.

Still, there is an unanswered question:

  • What if the melted ice wouldn’t have mixed with the Coke?
    I believe that the cup would have “runneth over” in that case. Maybe I’ll set up an experiment to verify this. Ice has a density of 917 kg/m3, so I’ll have to find a cheap fluid substance which doesn’t mix with water but which still has a higher density than ice. Cooking oil probably won’t do… Any suggestions?
    (I though about putting the ice cubes into little watertight rubber balloons instead. That would also prevent the two substances from mixing, but I’m afraid there would still be air inside my ballons.)
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