# Interesting estimates

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?

[spoiler]166 meters deep![/spoiler]

My Guess a kilometer

Source? (Or sauce?)

my guess is that it would be 3.5987kms thick

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.)

'Luthon64

The spoiler links to the source.

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

ds = (csfwdwρw)/((1-fw)ρs) ?

Perfect. Well done!

'Luthon64

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

Rigil

You didn’t mention the temperature :P. 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.

[spoiler]Molar mass of salt (NaCl) = 58.4 g/mol

.: 500 g of salt ≡ 500/58.4 = 8.562 mol NaCl
= 8.562 mol Cl (after dissociating the NaCl — will need heaps of energy for this!)
= 8.562÷2 = 4.281 mol Cl2.

Ideal gas law: p×V = n×R×T, whence V = n×R×T÷p

Putting in the values,

V = 4.281×8.314×298.15÷100,000 = 0.1061 m3 = 106.1 litres.

(That’s a lot!)[/spoiler]

'Luthon64

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?

Rigil

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?

[spoiler]More than 4600 million years. By the time you get there, Alpha Centauri may well be gone.

Edit: Due to being high on flu meds and general stupidity and carelessness, I made a gross arithmetic error in the above. The answer is in fact 46 million years.[/spoiler]

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.

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?

??? 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.

'Luthon64

That would make it somewhat cumbersome to dig out Johannesburg’s gold from the Hawaii side, but if the labour unrest continues …

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…

'Luthon64

True. Suddenly my calculation seems a bit opaque to me too. :-X

Here is one possible answer:

SA population is about 40,000,000 people.
Of which maybe 50% have access to a shower, i.e. 20,000,000 people.
Of which maybe 50% are prepared to urinate whilst showering, so 10,000,000 people.
Which they do maybe twice weekly. This gives 20,000,000 instances of not needing to flush a toilet per week.
Which comes to 1 billion saved flushes per year.
A toilet cistern holds maybe 8L of water.
So the annual water saving thanks to this slightly unsavoury activity comes to an estimated 8,000 megaliters per year.

Which is just over 6% of a major Eastern Cape water reserve, the Kouga dam!

Rigil

Quite possibly - I have been battling the flu and was high on meds. Let me go check those calculations…

Okay, here’s the new calculation:

Light travels at 300 000 km/s. So in a year, it travels 60 x 60 x 24 x 365 x 300 000 = 9 460 800 000 000 km.

Alpha Centauri is about 9 460 800 000 000 x 4.3 = 40 681 440 000 000 km from us. At 100 km/h it would take 406 814 400 000 hours to get there. Which is 16 950 600 000 days, and 46 440 000 years.

Better? I originally must have added zeros somewhere, or something - when I think now of the day I did this, I sort of see everything through a reddish fog of fever and coughing and drugs…

As you say, still a rather frightful distance - as bright as the stars are, I am sometimes surprised we can see any at all.

It is almost scarily amazing. And to think that you pick any star or far off galaxy and bring it into perfect focus with nothing but a stable atmosphere and a telescope. One has to marvel at the immense predictability with which light travels over even such vast distances.

Equally astounding to me is the sensitivity and range of the human eye, even in spite of it’s apparent “design” flaws.

Rigil

Which brings me to another question I have been wondering about, and which will ft neatly into this thread of estimates. Interstellar space isn’t completely empty. There is in fact a sort of interstellar “atmosphere” between us and the stars. Apart from nebulae, it is evidently not enough to blot out the stars, but how dense is the interstellar medium? How much gas is there between us and the nearest star, compared to what is in our own atmosphere?

Perhaps members with the necessary knowledge of this will want to post us some calculations and estimates.