A scientific question....
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Hello fellow 30's!! Sorry ah, Saturday night (actually Sunday morning already), can't sleep and got nothing better to do....
There are two beakers:
Beaker 1: contains one litre of milk
Beaker 2: contains one litre of kahlua
Ready?
A "certain volume" of kahlua is taken out from Beaker 2 and poured into Beaker 1, after which it is thorougly stirred. Then the same "certain volume" of this mixture is taken out from Beaker 1 and poured back into Beaker 2.
Is there more kahlua in the milk? Or more milk in the kahlua? -
100% kahlua into milk..
then taking out less than 100% kahlua back into the original...
beaker 2 has more kahlua than milk always until 100% is taken and put in the other beaker, stirred and poured back...
btw, leave the kahlua and milk undisturbed for a while, you'll find the whole stuff curdled
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at the start,Originally posted by gentlerock:Hello fellow 30's!! Sorry ah, Saturday night (actually Sunday morning already), can't sleep and got nothing better to do....
There are two beakers:
Beaker 1: contains one litre of milk
Beaker 2: contains one litre of kahlua
Ready?
A "certain volume" of kahlua is taken out from Beaker 2 and poured into Beaker 1, after which it is thorougly stirred. Then the same "certain volume" of this mixture is taken out from Beaker 1 and poured back into Beaker 2.
Is there more kahlua in the milk? Or more milk in the kahlua?
beaker 1 has 1 litre milk per 1 litre = concentration of milk = 1
beaker 2 has 1 litre kahlua per 1 litre = concentration of kahlua = 1
assume x litre of kahlua is poured from beaker 2 to beaker 1
beaker 1 now has 1+x litres
conc of milk in beaker 1 = 1/(1+x)
conc of kahlua in beaker 1 = x/(1+x)
beaker 2 now has 1-x litres
conc of milk in beaker 2 = 0
conc of kahlua in beaker 2 = 1
when x litre of mixture in beaker 1 is poured into beaker 2
both beakers now has 1 litre of mixture
conc of milk in beaker 1 = 1/(1+x) (unchanged)
conc of kahlua in beaker 1 = x/(1+x) (unchanged)
plotting graphs of y=1/(1+x) and y=x/(1+x)
1/(1+x) > x/(1+x) when x is between 0 and 1
therefore, conc of milk is always more than conc of kahlua in beaker 1 unless x = 1 litre (both will be equal in this case)
conc of milk in beaker 2 = 1/(1+x)*x = x/(1+x)
conc of kahlua in beaker 2 = x/(1+x)*x + 1-x = x²/(1+x)+ 1-x
plotting graphs of y=x/(1+x) and y=x²/(1+x)+1-x
x²/(1+x)+1-x > x/(1+x) when x is between 0 and 1
therefore, conc of kahlua is always more than conc of milk in beaker 2 unless x = 1 litre (both will be equal in this case) -
Originally posted by poon cho tang:at the start,
beaker 1 has 1 litre milk per 1 litre = concentration of milk = 1
beaker 2 has 1 litre kahlua per 1 litre = concentration of kahlua = 1
assume x litre of kahlua is poured from beaker 2 to beaker 1
beaker 1 now has 1+x litres
conc of milk in beaker 1 = 1/(1+x)
conc of kahlua in beaker 1 = x/(1+x)
beaker 2 now has 1-x litres
conc of milk in beaker 2 = 0
conc of kahlua in beaker 2 = 1
when x litre of mixture in beaker 1 is poured into beaker 2
both beakers now has 1 litre of mixture
conc of milk in beaker 1 = 1/(1+x) (unchanged)
conc of kahlua in beaker 1 = x/(1+x) (unchanged)
plotting graphs of y=1/(1+x) and y=x/(1+x)
1/(1+x) > x/(1+x) when x is between 0 and 1
therefore, conc of milk is always more than conc of kahlua in beaker 1 unless x = 1 litre (both will be equal in this case)
conc of milk in beaker 2 = 1/(1+x)*x = x/(1+x)
conc of kahlua in beaker 2 = x/(1+x)*x + 1-x = x²/(1+x)+ 1-x
plotting graphs of y=x/(1+x) and y=x²/(1+x)+1-x
x²/(1+x)+1-x > x/(1+x) when x is between 0 and 1
therefore, conc of kahlua is always more than conc of milk in beaker 2 unless x = 1 litre (both will be equal in this case)
ok..in that case i stick to Guiness
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Hmm - this takes a certain amount of thought.
First, the "certain amount" of Kahlua needs to be ascertained. Of course, with the viscosity of Kahlua, plus the evaporation rate of the various components of the substance, it would be fairly difficult to ascertain the exact amount poured from the amount left over.
Given the amount of alcohol content of Kahlua, it should be fairly easy to distill the mixture and determine the total amount poured into the milk, although you would have to ensure that temperature of the mixture is held at exactly 78.3 degrees Celsius, to prevent the evaporation of other substances from ruining the measurement. Considering the effects of surface tension, you would expect your estimates to be at abut 92.785% accuracy (given the condition of your lab equipment, of course - this is just a median estimate).
After all that trouble, you would realise that if you had exactly one litre of milk and one litre of Kahlua, and if a certain amount of Kahlua was taken out of its container, given its viscosity and the following amount that would be left over, there would be more milk than Kahlua.
At the end of this experiment, you would scull down the total amount of milk and Kahlua as a chaser to the six litres of beer I've ingested in the last four hours.
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PCT, you are good!Originally posted by poon cho tang:at the start,
beaker 1 has 1 litre milk per 1 litre = concentration of milk = 1
beaker 2 has 1 litre kahlua per 1 litre = concentration of kahlua = 1
assume x litre of kahlua is poured from beaker 2 to beaker 1
beaker 1 now has 1+x litres
conc of milk in beaker 1 = 1/(1+x)
conc of kahlua in beaker 1 = x/(1+x)
beaker 2 now has 1-x litres
conc of milk in beaker 2 = 0
conc of kahlua in beaker 2 = 1
when x litre of mixture in beaker 1 is poured into beaker 2
both beakers now has 1 litre of mixture
conc of milk in beaker 1 = 1/(1+x) (unchanged)
conc of kahlua in beaker 1 = x/(1+x) (unchanged)
plotting graphs of y=1/(1+x) and y=x/(1+x)
1/(1+x) > x/(1+x) when x is between 0 and 1
therefore, conc of milk is always more than conc of kahlua in beaker 1 unless x = 1 litre (both will be equal in this case)
conc of milk in beaker 2 = 1/(1+x)*x = x/(1+x)
conc of kahlua in beaker 2 = x/(1+x)*x + 1-x = x²/(1+x)+ 1-x
plotting graphs of y=x/(1+x) and y=x²/(1+x)+1-x
x²/(1+x)+1-x > x/(1+x) when x is between 0 and 1
therefore, conc of kahlua is always more than conc of milk in beaker 2 unless x = 1 litre (both will be equal in this case)
nice maths! -
MATH!!!!
run away SCREAMING!!!!!!!!!!!!!! -
Sorry, hunks and babes who have replied, sorry....I wasn't aware that so many replies had come in already. I was also out of the country for two days.
Ooooh.....Poon Cho Tang, you're really good!
When I was first asked the question, I just followed my instinct and said that there was more Kahlua in milk, than the other way. However, if you think about it, the non-mathematical way.....
Think about it the non-mathematical, logical way:
If you take X volume of Kahlua and pour it into the milk beaker....
You have to take X volume of milk and pour it into the Kahlua beaker....
Or else you will never end up at 1 litre per beaker again.
Thus, there are the same amounts of milk in kahlua, and kahlua in milk.
For the scientifically trained, conservation of mass applies here.
One think I learned about Club 30 though.....if this experiment was really conducted, only Poon Cho Tang would be sitting down doing the calculations. The rest would either walk away or will be having a drink. -
Scientific? IT"S MATHS!!! EEKS..
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having a drink?
more like 10