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Is Diet Soda Really Light?: Newsletter Challenge (March 2014)

Posted March 01, 2014 8:00 AM
Pathfinder Tags: challenge questions

This month's Challenge Question: Specs & Techs from GlobalSpec:

A can of a diet refreshment (such as a Diet Coke) and a can of regular refreshment (such as a regular Coke) are placed inside a bucket of water. Both cans contain exactly the same volume of liquid and the cans are identical in size and shape. Which can will float higher relative to the other?

And the answer is:

Sweetening regular soft drinks requires large amounts of sugar. The sugar will be dissolved in the liquid with only a small increase in volume. Remember also that the density of sugar water is greater than that of regular water. Diet drinks require artificial sweeteners to sweeten the drink, but a very small amount of the artificial sweetener will suffice. So the diet drink density is slightly heavier than regular water. Therefore the regular Coke will sink, or will at least float lower than the diet drink.

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#1

Re: Is Diet Soda Really Light?: Newsletter Challenge (March 2014)

03/01/2014 9:08 AM

Regular Coke will sink. The Diet Coke will float. The cause is the 35 grams of sugar in regular coke.

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#9
In reply to #1

Re: Is Diet Soda Really Light?: Newsletter Challenge (March 2014)

03/02/2014 10:37 AM

What is the reason for this experiment? If it is just weighing each can and using a water displacement to determine volume to have fun then fine to each his own. There is a nitrogen gas volume in each can also. That may vary at bit based on my Coca Cola working experience. Bottom line is neither should be consumed if you give a hoot for your bodily health.

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#2

Re: Is Diet Soda Really Light?: Newsletter Challenge (March 2014)

03/01/2014 11:02 AM

Wait till Monday- I'll check the specific gravities of each and publish them. The denser product will obviously displace more water and therefore ride lower. (Maybe I'll weigh the cans first too! Just to check their accuracy). By the way, you forgot to stipulate the temperature of each can has to be identical.

But I'm going to guess post #1 is right, we'll see for sure.

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#15
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Re: Is Diet Soda Really Light?: Newsletter Challenge (March 2014)

03/03/2014 10:54 AM

" The denser product will obviously displace more water "

- - - - Not if its inside a can. fill it with sand, the can still displaces a can of water.

The density or mass will only override the bouyancy of other can contents.

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#17
In reply to #15

Re: Is Diet Soda Really Light?: Newsletter Challenge (March 2014)

03/03/2014 11:01 AM

...except that the floating can does not displace a full can's volume of water.

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#19
In reply to #17

Re: Is Diet Soda Really Light?: Newsletter Challenge (March 2014)

03/03/2014 12:06 PM

Denser is denser. More mass per unit volume. Denser does not displace more water.

If you make the can or contents "denser" it will sink but the max water displacement is based on the CAN not the comtents within.

One must assume these are cans filled to standard volumes within.

A steel ball bearing is "denser" than a glass marble of the same size but does not displace more water.

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#21
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Re: Is Diet Soda Really Light?: Newsletter Challenge (March 2014)

03/03/2014 1:17 PM

Everything you say in this post is correct, BUT, since one can is floating, part of it is sticking out of the water, and that part does NOT displace any water.

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#22
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Re: Is Diet Soda Really Light?: Newsletter Challenge (March 2014)

03/03/2014 1:21 PM

We agree to disagree, based on definitions lol.

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#25
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Re: Is Diet Soda Really Light?: Newsletter Challenge (March 2014)

03/05/2014 1:03 AM

there's allways a bit of air in the can

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#29
In reply to #25

Re: Is Diet Soda Really Light?: Newsletter Challenge (March 2014)

03/11/2014 11:21 AM

The cans will sink to a level that will displace an equivalent weight of water.

Sugar may make the "coke" specific density higher than that of the Diet Coke, therefore more of the can will sink to displace an equivalent weight. The diet coke being of lower sp. grav. will float higher.

I think Archimedes got it right.

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#3

Re: Is Diet Soda Really Light?: Newsletter Challenge (March 2014)

03/01/2014 1:40 PM

Containers are filled by weight; some settling of contents may occur during shipping and handling.

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#4

Re: Is Diet Soda Really Light?: Newsletter Challenge (March 2014)

03/01/2014 3:36 PM
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#7
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Re: Is Diet Soda Really Light?: Newsletter Challenge (March 2014)

03/02/2014 9:31 AM

Dunking the cans in water only compares the RELATIVE specific gravities of the entire sealed containers. Other variables to consider are the weights of the cans, the amount of air trapped in the headspace of them, and the amount of CO2 dissolved in them.

The can manufacturing process might have slight variations from batch to batch. Possibly the cans might have even come from different factories. The filling process might be slightly off, too. Either of these might be significant compared to the slight difference of density between the two beverages.

Pour the beverages into a graduated cylinder and weigh them, but this depends on the accuracy of both methods.

Another way to measure the SG is with a narrow range hydrometer.

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#11
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Re: Is Diet Soda Really Light?: Newsletter Challenge (March 2014)

03/03/2014 7:47 AM

But the challenge was stated as, "Which can will float higher relative to the other?"

I think the pictured experiment resolves the question completely.

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#16
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Re: Is Diet Soda Really Light?: Newsletter Challenge (March 2014)

03/03/2014 10:57 AM

Only for that particular pair of cans, and only if both cans have been left sealed, and only if the liquid in the plastic container is pure water, and...

I'm pretty sure I could produce an unretouched photo showing the opposite, by puncturing the regular can and removing some liquid from it, then using an appropriate mixture of water, say with alcohol.

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#18
In reply to #16

Re: Is Diet Soda Really Light?: Newsletter Challenge (March 2014)

03/03/2014 11:36 AM

Now you're bending and breaking the rules........

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#20
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Re: Is Diet Soda Really Light?: Newsletter Challenge (March 2014)

03/03/2014 1:06 PM

Except one can is regular coke and the other is diet Dr. Pepper, so it only resolves the question between those specific beverages - which could have other differences besides the presence of real sugar. I've always found Dr. Pepper to contain more belches than coke.

Both are coke products though, so maybe not...

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#30
In reply to #11

Re: Is Diet Soda Really Light?: Newsletter Challenge (March 2014)

03/11/2014 11:37 AM

I already posted the same, except mine did not use diet dr. pepper in the example, but did in fact show diet coke vs. regular coke as the OP stated. I received a total snub, by not receiving any good answer marks. So thank you all very much.

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#5

Re: Is Diet Soda Really Light?: Newsletter Challenge (March 2014)

03/01/2014 4:14 PM

I thought it was supposed to be "The Pepsi Challenge".

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#13
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Re: Is Diet Soda Really Light?: Newsletter Challenge (March 2014)

03/03/2014 7:51 AM

Pepsi is talking to their lawyers on possible Coke infringement on their product.

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#6

Re: Is Diet Soda Really Light?: Newsletter Challenge (March 2014)

03/02/2014 3:37 AM

Presuming each can is full,there is no reason why the can would float, therefore the water displaced by the volume of each can would be exactly the same without variation. Both cans should sink to the bottom

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#8
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Re: Is Diet Soda Really Light?: Newsletter Challenge (March 2014)

03/02/2014 10:29 AM

That was my thought too. On the other hand, I have no idea of the density of whatever they add instead of sugar to the diet versions, nor of the effect on solubility of CO2 or other gasses. I don't drink either kind, so can't do the experiment myself...

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#12
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Re: Is Diet Soda Really Light?: Newsletter Challenge (March 2014)

03/03/2014 7:48 AM

The cans are never full when filled at the factory. There is always some air in the can.

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#23
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Re: Is Diet Soda Really Light?: Newsletter Challenge (March 2014)

03/05/2014 12:45 AM

Could it be that the word float is key to the answere If the cans were to sink displacement would be equal and there would be no variation. However if the cans were to float then the contents would determine how high one would float compared to the other,both cans contain beverage but one beverage contains more sugar than the other hence the variation Sugar is energy, energy is weightless therefore the can of coke wouldbe lighter and float higher

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#10

Re: Is Diet Soda Really Light?: Newsletter Challenge (March 2014)

03/03/2014 2:04 AM

Oh, how many things are wrong with this question?

A bucket is not sufficient to measure differences in density unless one of the items under test is less dense than water and one is more dense. If both are more dense than water, they will both descend to the bottom of the bucket. If you want a proper comparison, you would need a much, much taller column of water, such that there is a significant difference in the density of water between top and bottom. You don't get Cartesian Divers without very carefully filling the bottles, and beverage cans are probably not perfectly filled to function in that way.

Note that the question does not require a comparison of two mixtures identical except for a single ingredient. The question is simply comparing a diet beverage and a regular beverage. Two similarly branded products are offered as examples, but even those two have very different formulas; heck, formulations of Diet Coke vary depending on what country it's sold in. So really, the question being asked is if all diet beverages have a lower specific gravity than all non-diet beverages. Compare a can of water (which is an unsweetened, low-calorie beverage) to a can of Hawaiian Punch...sure enough, the HP has a higher SG and it sinks. But we cannot induce from that example that all diet drinks are lighter than regular drinks.

However, the title of the post, at least, refers to "Diet Soda" which can lead one to assume that the OP means that the beverages in question must be carbonated. Since even carbonated beverages vary widely in formulation, we cannot scientifically compare one soda to another without knowing the recipes of both. If some scientifically-minded Coca-Cola employee would be so kind as to post the formulae for Classic Coke and Diet Coke, we would be much obliged. For science.

There is a belief, common at least among people who are not soda manufacturers, that diet sodas are more carbonated than regular. I'm not a soda manufacturer either, so I don't know if it's true. If that is indeed the case, then the regular soda would have a larger SG and would sink further.

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#14

Re: Is Diet Soda Really Light?: Newsletter Challenge (March 2014)

03/03/2014 10:28 AM

Based on the qualifying statements in the OP's challenge, I believe there are still variables out of control: (1) is there ambient light incident on the cans? Nevertheless, I will make my assertion here that the diet coke will ride just a bit higher, since it takes less weight of the artificial sweetener than it does sugar. In other words, it will be correct that the syrupy regular soda is more dense than the diet version. Cans can be assumed identical with identical volumes of liquid in them for the purposes of this discussion. I Googled the answer:

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#34
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Re: Is Diet Soda Really Light?: Newsletter Challenge (March 2014)

03/25/2014 6:54 PM

Try two cans of same kind, let's say regular. Shake one of them before floating it. The can may bulge slightly tending to the maximum volume minimum area (sphere) and thus float higher. Just another parameter between the light momentum reflecting off the can. Diet Coke may be more sensitive, I am thinking of the Diet Coke bottle and pimentos experiment.

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#24

Re: Is Diet Soda Really Light?: Newsletter Challenge (March 2014)

03/05/2014 12:59 AM

if there's no replacement for the sugar in the regular refreshment, the light version of the refreshment floats higher, if there's a replacement for the sugar than it depends on the weight of the refreshment and the sugar.

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#26
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Re: Is Diet Soda Really Light?: Newsletter Challenge (March 2014)

03/05/2014 9:32 AM

Is that regular oxymoron, or a de-oxygenated oxymoron? Please take a deep breath and try again. How is it you will argue with a photograph showing the results of the experiment? Obviously, an unwise choice.

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#27
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Re: Is Diet Soda Really Light?: Newsletter Challenge (March 2014)

03/06/2014 1:18 AM

?

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#28

Re: Is Diet Soda Really Light?: Newsletter Challenge (March 2014)

03/11/2014 10:02 AM

The artificial sweetener in the diet soda is much less dense than the sugar in the regular soda.

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#31

Re: Is Diet Soda Really Light?: Newsletter Challenge (March 2014)

03/16/2014 6:18 PM

Will a can of normal coke and a can of diet coke differ in their buoyancy in water, all other things held equal and assuming no air spaces in the full cans. This would be an easy question if volumes of solutes and solvents added when brought together. Just calculate the quantity of sugar and water, and sweetner and water, in the fixed volume of the drink cans, calculate the relative weights, and you have your answer. Their relative densities compared with water, would indicate if they both float, one higher than the other, one floats and one sinks, or both sink, taking into account the amount of water displaced by the empty cans.

But the volumes of solutes and solvents do not add - indeed, adding a volume of ethanol to water can reduce the overall volume. With sugar, it probably increases the volume when added to water, but by an amount less that ithe sugar's initial volume. So a correction factor is needed, in addition to taking into account the relative densities of sugar and water.

So the answer will depend on the relative quantities of sugar (10.5 tea spoons?) in the coke and sweetner in the diet coke (small or negligible?), their contribution to the overall equal volume of liquid in the cans (not additive) and the consequent relative masses of the final liquid in the cans.

Good luck on that one. You could do the experiment, but explaining the result would require the above rather complex considerations. My guess is that the regular coke would sink more heavily than diet coke because of the added weight of the 10.5 teaspoons of sugar would not be offset enough by the compaction in solution. Sugar sinks and swirls on the bottom when I add it to my tea and stir.

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#32

Re: Is Diet Soda Really Light?: Newsletter Challenge (March 2014)

03/19/2014 2:41 AM

Sugar added to water increases the density of the solution, not the volume. Other sweeteners (e.g., corn syrup) will not. (Most will decrease it.) The cans are of the same volume and are filled with the same volume of fluid, so the sugared drink will be heavier/denser and will 'float' lower in a bucket of water.

Note increase of density with amount of sugar present.

http://wiki.houptlab.org/wiki/Density_of_Sugar_Solutions

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#33

Re: Is Diet Soda Really Light?: Newsletter Challenge (March 2014)

03/25/2014 10:26 AM

The can with the most air in it will rise higher than the other.

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#35

Re: Is Diet Soda Really Light?: Newsletter Challenge (March 2014)

03/25/2014 9:03 PM

There is insufficent information provided to answer this question. The can size and shape are identical but material of construction and can material density is not stated. This leads on to the question "Does the mass of each combined can and contents exceed the mass of water displaced" - if the answer is yes for both then obviously neither can will float higher than the other. If the answer is no, then both cans will float. If they float we need to know the combined mass of each to be able to answer the question. If the can masses (and volumes which is implicit in the statement "they are the same size and shape") are identical then we need to know the (bulk) densities of the contents at whatever pressure the cans are "operating" at and the volume of liquid in each can. Without answers to these questions, at best we can only guess. Not clear in the task provided is does the pressure in the can have a bearing on its volume - the comment "same size and shape" infers that volumes are identical but ......

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#36

Re: Is Diet Soda Really Light?: Newsletter Challenge (March 2014)

03/25/2014 11:54 PM

The answer may depend on the distinction between ounces (weight) and fluid ounces (actually volume). If each can contains 12 fluid ounces, the denser one will weigh more.

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#37

Re: Is Diet Soda Really Light?: Newsletter Challenge (March 2014)

03/26/2014 4:57 PM

The water in the bucket is not compressable and is of a uniform density (weight per unit volume). If the density of the cans is more than the water (about 1 gram per millilitre), they will sink. If less, they will float to a height that displaces their weight in water.

The soda formula with the lower density will float higher. (sugar solution or aspartame?)

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#38

Re: Is Diet Soda Really Light?: Newsletter Challenge (March 2014)

03/26/2014 5:13 PM

May I suggest that before replying, the older comments should be read. There is a lot of posts that seem to be obvious and redundant. Yes, soda formula with the lower density will float higher. That is because of specific gravity, which is the main concept involved.

Bottom line, the most accurate way to determine the density or SG is with a floating densitometer. Leaving the beverage in question inside the cans involve far too many additional variables.

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