I’m sure this must have been bought up before but perhaps my search powers are week…
One of my favourite little factoids is this: Take a glass dip it in the sea and then magically tag every atom in the water. Pour the water back in and wait several years for the water cycle to churn everything up. Go to any source of water on Earth and dip your glass back in and there will be an evens chance of having one of the original atoms back in your glass.
In other words, there are as many atoms in a glass of water as there are glasses worth of water on Earth. I guess this is a variation of the Ceaser’s Last Breath theory.
So firstly, is this actually true? Have I expressed it properly? And if I have I want to know, what sort of size glass are we talking about here? For instance, could I use a pint glass and change the language to say that there is a high possibility of recapturing one of my original atoms?
A larger glass means that a) more atoms get tagged and b) more atoms get scooped up the second time around. So you could pose the question: what size glass do you need to have a 50% chance of getting one of your original atoms?
2.4 x 10^25, assuming a 1 - cup glass. For the rest of your question, you’ll have to wait for someone with more knowledge about how much water is in the world than me.
I thought it was usually phrased as “molecule of water”, not atom. And assumed that a single molecule of water was well-defined, and constant, which is a bad assumption, what with molecules being broken up and reformed, even in a cup of water just sitting on your counter.
Using atoms would be a little better defined, but you’d still have those atoms changing from water to other materials. I assume you’d ignore that for the OP.
According to this, there is 326,000,000,000,000,000,000 gallons of water in the world, or about 5.2 x 10^21 cups, meaning about 4600 molecules per cup, subject to all ZenBeam’s provisos.
According to [url=]this site, there are 1,386,000,000 cubic kilometers of water on Earth (or, more accurately, there would be if it was all liquid. This works out to 4.6 x 10[sup]46[/sup] water molecules.
A glass of water contains, say, a half-liter of water. This is 1.6 x 10[sup]25[/sup] water molecules.
So the chance that a given molecule on the Earth gets caught up in your first glass is one in 2.9 x 10[sup]21[/sup]. But there are about 5000 times more water molecules in your second glass than that number, so there would be about 5000 water molecules in your first glass that were also in your second glass.
If I’ve done my math correctly, using the same logic you’d need a cup with a volume of 6.4 milliliters in order to expect to get one atom from your first glass into your second glass.
which equals 1.35465909 × 10^23 cubic centimeters. Let’s say the glass is a half liter (500 grams/cubic centimeters) we have 2.7093182e+20 glasses of water on Earth.
Sixteen grams of water is a mole, so 500 grams would be 31.25 moles. Multiplying 31.25 x 6.02x10^23 = 1.88125e+25 molecules of water in a glass, so there are about 70,000 times as many water molecules in a glass as there are glasses of water on Earth.
So, then, the real crux of the matter. Does anyone know the atmospheric science to figure out a mean length of time for your first glass to evenly distribute itself across the globe? Obviously, if you take a glass of water from a tap in New Jersey, toss it into the ocean, then fly to Australia the next day and scoop up a glass of water from the Australian coast, there is essentially a 0% chance of anything from that first glass ending up in your second glass.
So how long does it take? 4 weeks? 1 year? 20 years?
Try up to 20,000 years, and that is an average; glaciers contain ice that can be (at least) 800,000 years old. Groundwater can take 10,000 years or more as well, and the oceans take about 3,200 years for the thermohaline circulation to recycle the water. However, if the glasses are taken from the surface of the ocean, many of the original water molecules are probably still near the surface since only the upper layers of the ocean are well-mixed (for example, it gets colder as you go down further, so the water doesn’t have any tendency to rise and mix, unless it is forced to do so by upwelling). So I’d say that you’d probably get more original water molecules than expected in the second glass.
I know molecules are really small and all, but I still find it pretty mindboggling that there are thousands of times more molecules in a glass of water than there are glasses of water on the entire planet.
That picture looks like not nearly enough water. I known its supposed to be spherical, but still. Might be more effective if they showed the ball of water on the edge to see height.
Remember, the oceans are really shallow, relative to the size of the Earth. The oft-quoted stat is that if you scaled the naked Earth down to snooker ball size, it would be smoother than a regulation cue ball.
Yeah…I realize it’s showing a ball with a diameter of 2000 miles or so, which is insane, and would stretch well out of the earth’s atmosphere, but it’s hard to visualize that with the angle they chose for the graphic. Which is why I think it would be more effective if they showed a lower angle.
Spheres showing:
(1) All water (sphere over western U.S., 860 miles in diameter)
(2) Fresh liquid water in the ground, lakes, swamps, and rivers (sphere over Kentucky, 169.5 miles in diameter), and
(3) Fresh-water lakes and rivers (sphere over Georgia, 34.9 miles in diameter).
