Mintaka Posted December 21, 2010 Report Posted December 21, 2010 I was watching British TV programme QI, hosted by Stephen Fry who made the claim in the title of this post. Can this be true? It sounds impossible. Is it? Quote
CraigD Posted December 22, 2010 Report Posted December 22, 2010 More Water Molecules In A Glass Of Water Than Grains Of Sand On EarthI was watching British TV programme QI, hosted by Stephen Fry who made the claim in the title of this post. Can this be true? It sounds impossible. Is it?Let’s try some estimation and see! :) Let’s assume a “glass of water” contains about 0.25 kg of water. Dividing by the molecular mass of a water molecule, 18 AMU = 3.0e-26 kg, we get the number of water molecules in a glass of water = 8.3e24 . The dividing line between dirt, sand, and gravel is vague and somewhat arbitrary, but a common standard is that a sand grain has diameter between 7.4e-5 to 6.3e-4 m. Assuming a spherical shape, we get a volume of 2.1e-13 to 1.3e-10 m3 and a density about that of water, a mass of 2.1e-10 to 1.3e-7 kg. Now, the question becomes, how much sand is there on Earth? Let’s assume the whole Earth is covered with a uniform layer of sand 1 m deep. (As we'll see later, this is likely a big overestimate) The Earth’s lithosphere has a mass of about 2.8e22 kg, and averages about 70000 m thick, so this layer would mass about 4e17 kg. Dividing this mass by the mass of a grain of sand give us the number of grains of sand on Earth = 1.9e27 to 3.1e24 . I’ve likely overestimated the amount of sand on Earth by a factor of 3000 to 2000000 – most sources estimate that there are about 1e21 grains of sand on Earth. But even my big estimate shows Fry’s claim to be possibly. If one were to undertake the huge engineering project of grinding vast quantities of rock into sand, though, it’s just possible you could make a liar of him! ;) Fun stuff, Mintaka - and welcome to hypography! :thumbs_up modest, Ken and JMJones0424 3 Quote
Mintaka Posted January 10, 2011 Author Report Posted January 10, 2011 CraigD!Thank you! It's hard for me to understand the numbers ( makes more sense to me when you use 'trillions' ;-) But the fact this mind-boggling statement seems to be true, is truly incredible. Amazing... Thanks again! M. Let’s try some estimation and see! :) Let’s assume a “glass of water” contains about 0.25 kg of water. Dividing by the molecular mass of a water molecule, 18 AMU = 3.0e-26 kg, we get the number of water molecules in a glass of water = 8.3e24 . The dividing line between dirt, sand, and gravel is vague and somewhat arbitrary, but a common standard is that a sand grain has diameter between 7.4e-5 to 6.3e-4 m. Assuming a spherical shape, we get a volume of 2.1e-13 to 1.3e-10 m3 and a density about that of water, a mass of 2.1e-10 to 1.3e-7 kg. Now, the question becomes, how much sand is there on Earth? Let’s assume the whole Earth is covered with a uniform layer of sand 1 m deep. (As we'll see later, this is likely a big overestimate) The Earth’s lithosphere has a mass of about 2.8e22 kg, and averages about 70000 m thick, so this layer would mass about 4e17 kg. Dividing this mass by the mass of a grain of sand give us the number of grains of sand on Earth = 1.9e27 to 3.1e24 . I’ve likely overestimated the amount of sand on Earth by a factor of 3000 to 2000000 – most sources estimate that there are about 1e21 grains of sand on Earth. But even my big estimate shows Fry’s claim to be possibly. If one were to undertake the huge engineering project of grinding vast quantities of rock into sand, though, it’s just possible you could make a liar of him! ;) Fun stuff, Mintaka - and welcome to hypography! :thumbs_up Quote
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