## South African Skeptics

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# Interesting estimates

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Rigil Kent
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 « on: January 03, 2013, 09:45:19 AM »

Came across an interesting estimate.

Imagine that you've extracted all of the salt from all of the oceans and sprinkled it over all of the world's dry land masses. How deep would such a layer of salt be?

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cr1t
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 « Reply #1 on: January 03, 2013, 10:33:29 AM »

My Guess a kilometer
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st0nes
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 « Reply #2 on: January 03, 2013, 11:02:36 AM »

Came across an interesting estimate.

Imagine that you've extracted all of the salt from all of the oceans and sprinkled it over all of the world's dry land masses. How deep would such a layer of salt be?

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Source? (Or sauce?)
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Brian
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I think therefor I am, I think

 « Reply #3 on: January 03, 2013, 11:06:00 AM »

my guess is that it would be 3.5987kms thick
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Mefiante
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 « Reply #4 on: January 03, 2013, 11:17:56 AM »

Using the following rough data estimates (drawn from memory):
• Ocean salinity (by mass) cs = 3% = 0.03
• Fraction of Earth’s surface covered in sea/ocean fw = 70% = 0.7
• Average ocean depth dw = 3,000 metres
• Ocean water density ρw = 1 ton/m3
• Density of granular salt ρs = 1.3 ton/m3

yields a salt depth of ds = 162 metres.

(I leave it as an exercise for the reader to derive the simple formula relating ds to the other variables.)

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Rigil Kent
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 « Reply #5 on: January 03, 2013, 11:50:01 AM »

Source? (Or sauce?)
The spoiler links to the source.

I must say, the answer leaves me a bit annoyed about the inflated price of table salt!

I leave it as an exercise for the reader to derive the simple formula
ds = (cs*fw*dw*ρw)/((1-fw)*ρs) ?
 « Last Edit: January 03, 2013, 12:09:37 PM by Rigil Kent » Logged
cr1t
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 « Reply #6 on: January 03, 2013, 11:58:55 AM »

Using the following rough data estimates (drawn from memory):
• Ocean salinity (by mass) cs = 3% = 0.03
• Fraction of Earth’s surface covered in sea/ocean fw = 70% = 0.7
• Average ocean depth dw = 3,000 metres
• Ocean water density ρw = 1 ton/m3
• Density of granular salt ρs = 1.3 ton/m3

yields a salt depth of ds = 162 metres.

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Mefiante
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 « Reply #7 on: January 03, 2013, 14:29:29 PM »

ds = (cs*fw*dw*ρw)/((1-fw)*ρs) ?
Perfect.  Well done!

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Rigil Kent
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 « Reply #8 on: June 13, 2013, 16:51:22 PM »

Staying with the halides: What volume of potential chlorine gas, at atmospheric pressure, is locked up in a 500g packet of table salt?

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Mefiante
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 « Reply #9 on: June 13, 2013, 18:16:59 PM »

You didn’t mention the temperature .  It’s equally important.  I’ll assume (1) standard ambient temperature and pressure (SATP) conditions (25 °C and 100 kPa = 0.986 atm), and (2) that molecular chlorine gas (Cl2) behaves like an ideal gas at SATP conditions.

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Rigil Kent
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 « Reply #10 on: June 14, 2013, 10:25:27 AM »

Very good. (I did it like this: (36/58)(500/58)moles x 22.4 cdm/mole = 120cdm.)

OK, something with a more speculative answer: How much water does South Africa save every year due to people peeing in the shower?

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brianvds
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 « Reply #11 on: June 14, 2013, 14:18:57 PM »

I did some back-of-an-envelope calculations for a star gazing evening I am going to have at the school where I work.

If you dug a tunnel through the center of the Earth, it would take over five days to drive a car through it at 100 km/h (and no rest stops).

At the same speed, it would take more than five months to reach the Moon.

And to get to Saturn (seeing as Saturn is one of the planets that will be visible)? More than a thousand years. If you started driving at around the time of the fall of Rome, you'd be getting to Saturn now.

But how long to drive to the nearest star?

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Mefiante
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 « Reply #12 on: June 14, 2013, 14:45:50 PM »

(I did it like this: (36/58)(500/58)moles x 22.4 cdm/mole = 120cdm.)
Hmm, I must challenge the leading factor “(36/58)” (≈ 0.621).  Presumably this is the molar mass ratio of Cl to NaCl, and, if so, the reason for using it is opaque to me.

Here’s why:  500 g of salt corresponds to 500/58 = 8.62 moles of NaCl.  Since each NaCl molecule contains a single Cl atom, completely dissociating the NaCl must then yield exactly 8.62 moles of atomic Cl, and the Na portion is no longer of any further interest.  However, since chlorine normally exists as a diatomic molecular gas, i.e. as Cl2, each mole of atomic Cl yields 0.5 moles of molecular chlorine gas.  Therefore, the factor in question should be 0.5, and your result would then become 96.6 dm3 = 96.6 litres (22.4 litres being the volume of one mole of an ideal gas at STP, not SATP).  If I use STP rather than SATP in my calculation, the temperature and pressure to use are 273.15 K and 101.325 kPa (= 1 atm) respectively, and my result is then 95.9 litres, which differs by 0.7% from yours.  This difference is readily explained by the slightly different molar weights for salt that were used.

How much water does South Africa save every year due to people peeing in the shower?
A few million bladder-days’ worth, roughly the same amount consumed in bars and restaurants.  Or do you want that in units of camel humps per kidney failure?

But how long to drive to the nearest star?
Are you sure you calculated correctly?  I get an answer that is 1/100th of that which you give — still a very long time, though.

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Hermes
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 « Reply #13 on: June 14, 2013, 17:07:01 PM »

If you dug a tunnel through the center of the Earth, it would take over five days to drive a car through it at 100 km/h (and no rest stops).
That would make it somewhat cumbersome to dig out Johannesburg's gold from the Hawaii side, but if the labour unrest continues ...
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Mefiante
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In solidarity with rwenzori: Κοπρος φανεται

 « Reply #14 on: June 14, 2013, 17:31:33 PM »

Forget about gold mining and think of tourism instead.  Such a tunnel would make for the ultimate bungee jump ’cos you would be able to do it without any cord being attached to your ankles!  You’d have to do it at night by launching yourself off the edge and aiming for the very faint speck of light about 12,500 km away.  You’d bounce back and forth for a good few hours and any self-respecting thrill-seeker would no doubt have a fun time of it.

There are two obvious disadvantages, though. First, you’d be in a really warm place when you finally stopped bouncing, and (2) getting back to surface again would require a jet plane.  Still, the resultant cost would make the jump available only to the very wealthiest clients and so you won’t have to worry about setting up a call centre or a complaints line…

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