1. ## Mixed Up

I have two contains that both hold 2 litres of liquid. In the first, I place 1 litre of red wine. In the other, I place 1 litre of white wine. I then take a cup and scoop exactly 100 ml (1/10 of a litre) from the red wine and place it in the white wine container. I then stir the white wine container so it is very well mixed and scoop exactly 100ml of the resultant mixture and place that in the red wine container.

Question: Is there more red wine in the white wine container, or is there more white wine in the red wine container?

2. ## Re: Mixed Up

<span style="background-color: #FFFF00; color: #000000; font-weight: bold"><font color=yellow>Neither option is correct. The concentrations of red wine in white and white wine in red are the same.</font color=yellow></span hi>

3. ## Re: Mixed Up

<span style="background-color: #FFFF00; color: #000000; font-weight: bold"><font color=yellow>Assuming that there is no volume loss when mixing red and white wine, the volume in each container at the end is the same as in the beginning. So there must be as much red wine in the white wine container as there is white wine in the red wine container. This is independent of both the size of the containers and of the amount transferred.</font color=yellow></span hi>

4. ## Re: Mixed Up

The question is best posed with MASS not volumes. As mentioned in the answers, one must assume that the volumes stay the same: which might not be true.

Steve

5. ## Re: Mixed Up

Yes, HansV certainly hit the nail on the head! And is the 'assumption' really needed as I went to all the effort to specify 'exactly' all the time?

6. ## Re: Mixed Up

With red and white wine it is probably not relevant, but with some fluids, a mixture takes up less volume than the individual amounts. In each fluid separately, the molecules keep at a certain distance from each other. In a mixture, the molecules of fluid A may occupy spaces left by the molecules of fluid B and vice versa. Mixing a bit of fluid A into a large volume of fluid B need not be symmetric with mixing a bit of fluid B with a large volume of fluid A. So you would not necessarily end up with 1 litre in each container. However, if you have 1 kg of each fluid, and transfer 100 g from A to B, mix thoroughly, then transfer 100 g back, you end up with 1 kg in each container. (There is still an assumption, of course: that the fluids don't react with each other. If the mixture is explosive, the results are quite different.)

7. ## Re: Mixed Up

But even with explosion/reactions the masses will always balance (conservation of mass: mass is never created nor destroyed); (though this could affect the answer to the question posed!)

Volumes can (and often do) change in these type of mixing. SInce wine is mostly water and should have simila alcohol contents it might be immaterial, but if the wines were different proof or you were using 2 different chemicals (other than primarily water as we have been posed) the total volume could be less than or even more than the sum of the individual volumes (some even by a significant amount)

Steve

8. ## Re: Mixed Up

Thanks. I meant that there might remain less than 1 kg within each container as a result of a possible reaction, not that mass would disappear.

9. ## Re: Mixed Up

I understood what you meant, I just wanted to clarify for anyone "science-challenged" <img src=/S/grin.gif border=0 alt=grin width=15 height=15>

Losing the mass in the container would change the response to the quesion as posed. It might even lose the container making the question moot.

Steve

10. ## Re: Mixed Up

I suspect carrying out the experiment in the location of Claude's cellar would certainly result in a mass change in the volume.... <img src=/S/laugh.gif border=0 alt=laugh width=15 height=15>

11. ## Re: Mixed Up

Like:

You want to perform a scientific experiment with white and red wine.

You go down into the wine cellar and open one bottle of excellent white wine and one bottle of excellent red wine.
You pour one glass of white wine and sample it.
You decide it's far too good to mix it with the red wine, so you finish it.
You pour one glass of red wine and sample it.
This one, too, is far too good to be mixed, so you finish it.

Four bottles later, you stumble, and red and white wine get mixed up on the cellar floor.
You are not in a condition to draw any conclusions any from this any more.

...

Next day, you remember that you wanted to perform a scientific experiment with white and red wine.

You go down into the wine cellar and ...

12. ## Re: Mixed Up

A related experiment (don't try this at home, it is only a "thought experiment") is to take a 1 kg of excrement and a 1 kg of of wine.

You will discover that if you take some mass "x" of wine (x > 0) and put it into the excrement, mix well, and then take out that same mass "x" of the excrement/wine mixture, and put it into the wine, that when you are done you have you will have 2 kg of excrement no matter what x is <img src=/S/grin.gif border=0 alt=grin width=15 height=15>.

Steve

13. ## Re: Mixed Up

<img src=/S/yikes.gif border=0 alt=yikes width=15 height=15>

I'll restrict myself to experiments with wine.

14. ## Re: Mixed Up

That is an experiment with wine (or did you mean "just wine"?)

Steve

15. ## Re: Mixed Up

Hiccup. I meant jusht wine. Thanksh.

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